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Exploratory Research Project PN-II-ID-PCE-2011-3-0024

 

Contract: 157/05.10.2011, financed by UEFISCDI – Romanian Executive Agency for Higher Education, Research, Development and Innovation

 

Project duration: 5 years (5/10/2011 – 4/10/2016)

 

Project title: The structure and sensitivity of the solution sets of variational inequalities, optimization and equilibrium problems under generalized monotonicity

 

Project manager: Professor Gábor KASSAY, Ph.D.

 

            Babeş-Bolyai University, Cluj-Napoca

            Faculty of Mathematics and Computer Science

            Department of Mathematics

            1, Kogălniceanu Street

            400084 Cluj-Napoca, Romania

 

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Down Arrow Callout: Research team

Down Arrow Callout: Project summary and objectives

Down Arrow Callout: Publications

Down Arrow Callout: Conferences 
and seminars

Down Arrow Callout: PhD/habilitation dissertations

Down Arrow Callout: External collaborators

Down Arrow Callout: Annual 
scientific reports

 

 

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Research team

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image013.jpg

Prof. Gábor KASSAY, Ph.D. – project leader

E-mail: kassay [ at ] math [ dot ] ubbcluj [ dot ] ro

URL: http://math.ubbcluj.ro/~kassay/

 

 

 

 

image014.jpg

Prof. Nicolae POPOVICI, Ph.D. habil.

E-mail: popovici [ at ] math [ dot ] ubbcluj [ dot ] ro

URL: http://math.ubbcluj.ro/~popovici/

 

 

 

 

image015.jpg

Assoc. prof. Cornel PINTEA, Ph.D.

E-mail: cpintea [ at ] math [ dot ] ubbcluj [ dot ] ro

URL: http://math.ubbcluj.ro/~cpintea/

 

 

 

 

image016.jpg

Assoc. prof. Szilárd LÁSZLÓ, Ph.D.

E-mail: laszlosziszi [ at ] yahoo [ dot ] com

URL: http://www.researcherid.com/rid/E-9509-2011

 

 

 

 

image017.jpg

Assist. prof. Mihaela MIHOLCA (BERCHEŞAN), Ph.D.

member of the project team since 01/11/2012

E-mail: mihaela.miholca [ at ] yahoo [ dot ] com

URL: http://math.ubbcluj.ro/~mmiholca

 

 

 

takacs.png

Petra-Renáta TAKÁCS, Master Student

Member of the research team since 01/02/2016

E-mail: t_petra92 [at] yahoo [dot] com

URL:

Former member

Erika NAGY, Ph.D.

member of the project team till 31/12/2014

E-mail: na.erika [ at ] yahoo [ dot ] com

 

Former member

 

 

Boglárka BURJÁN-MOSONI, Ph.D.

member of the project team till 31/10/2012

E-mail: mo_bogi [ at ] yahoo [ dot ] com

 

 

 

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Project summary and objectives

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The project is mainly motivated by the growing literature in scalar and vector optimization problems, variational inequalities, and equilibrium problems, which neatly shows that these fields are appropriate for applying the modern tools of variational analysis. Nine objectives are considered:

 

O1.Studying condition numbers and metric regularity within parametric variational inequalities and parametric equilibrium problems;

O2.Identifying classes of generalized monotone operators for which local and global monotonicity are equivalent and deduce injectivity results;

O3.Studying the structure of the solution sets for generalized monotone operators;

O4.Characterizing the subdifferential for certain classes of generalized monotone operators;

O5.Approaching the sum problem for maximal monotone operators;

O6.Constructing algorithms for variational inequalities and equilibrium problems;

O7.Extending the proximal point algorithm for equilibrium problems to reflexive Banach spaces;

O8.Characterizing generalized convex vector functions by scalarization;

O9.Studying the structure of the solution sets of vector variational inequalities and equilibrium problems.

 

 

 

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Publications

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Period

Papers published/accepted in ISI journals

Papers published/accepted in journals indexed in international databases

Papers under review

Total

05.10.2011 – 15.12.2011

1 [item P1 in the list below]

0

0

1

16.12.2011 – 15.12.2012

7 [items P2-P8 in the list below]

0

0

7

16.12.2012 – 15.12.2013

7 [items P9-P13 and P15-P16 in the list below]

1 [item P14 in the list below]

0

8

16.12.2013 – 31.12.2014

9 [items P17-P23, P25 and P26 in the list below]

1 [item P24 in the list below]

0

10

01.01.2015 – 31.12.2015

6 [items P27, P29 -P33 in the list below]

0

1 [item P28 in the list below]

7

01.01.2016 – 04.10.2016

1 [item P34 in the list below]

-

2[items P35 and P36 in the list below]

3

Total

31 (sum of impact factors: 29,385)

2

3

36

 

P1.         Szilárd László and Boglárka Burján-Mosoni: About the maximal monotonicity of the generalized sum of two maximal monotone operators, Set-Valued Var. Anal., 20 (2012), 355-368, doi:10.1007/s11228-011-0202-z [JCR Science Edition 2015 IF: 0,973]

P2.         Regina Burachik and Gábor Kassay: On a generalized proximal point method for solving equilibrum problems in Banach spaces, Nonlinear Anal., 75 (2012), 6456-6464, doi:10.1016/j.na.2012.07.020 [JCR Science Edition 2015 IF: 1,125]

P3.         Monica Bianchi, Gabor Kassay and Rita Pini: An inverse map result and some applications to sensitivity of generalized equations, J. Math. Anal. Appl., 399 (2013), 279-290, doi:10.1016/j.jmaa.2012.10.023 [JCR Science Edition 2015 IF: 1,014]

P4.         Gabor Kassay, Cornel Pintea and Szilárd László: Monotone operators and first category sets, Positivity, 16 (2012), 565-577, doi:10.1007/s11117-012-0193-5 [JCR Science Edition 2015 IF: 0,479]

P5.         Szilárd László: Existence of solutions of inverted variational inequalities, Carpathian J. Math., 28 (2012), 271-278, webpage [JCR Science Edition 2015 IF: 0,610]

P6.         Szilárd László: On the strong representability of the generalized parallel sum, Bull. Malays. Math. Sci. Soc., 37 (2014) (4), 1029-1046 [JCR Science Edition 2015 IF: 0,640]

P7.         Alireza Amini-Harandi and Szilárd László: A coincidence point result via variational inequalities, Fixed Point Theory 15 (2014) (1), 87-98 [JCR Science Edition 2015 IF: 0,581]

P8.         Mihaela Miholca (Bercheşan): On set-valued optimization problems and vector variational-inequalities, Optim. Lett., 8 (2014) (2), 463-476, doi:10.1007/s11590-012-0591-4 [JCR Science Edition 2015 IF: 1,019]

P9.         Cornel Pintea: Global injectivity conditions for planar maps, Monatsh. Math., 172 (2013), 399-413, doi:10.1007/s00605-012-0474-x [JCR Science Edition 2015 IF: 0,664]

P10.     Mihaela Miholca (Bercheşan): Vector variational-like inequalities and vector optimization problems, Carpathian J. Math., 30 (2014) (1), 101-108, webpage [JCR Science Edition 2015 IF: 0,610]

P11.     Radu Ioan Boţ, Ernö Robert Csetnek and Erika Nagy: Solving systems of monotone inclusions via primal-dual splitting techniques, Taiwanese J. Math., 17 (2013) (6), 1983-2009, doi:10.11650/tjm.17.2013.3087 [JCR Science Edition 2015 IF: 0,617]

P12.     Gabor Kassay and Mihaela Miholca (Bercheşan): Existence results for variational inequalities with surjectivity consequences related to generalized monotone operators, J. Optim. Theory Appl., 159 (2013), 721-740, doi:10.1007/s10957-013-0383-8 [JCR Science Edition 2015 IF: 1,160]

P13.     Dorin Andrica, Dana Mangra and Cornel Pintea: The circular Morse-Smale characteristic of closed surfaces, Bull. Math. Soc. Sci. Math. Roumanie, Tome 57(105) (2014) (3), 235–242, [JCR Science Edition 2015 IF: 0,395]

P14.     Dorin Andrica, Dana Mangra and Cornel Pintea: The minimum number of critical points of circular Morse functions, Stud. Univ. Babes-Bolyai Math., 58 (2013 (4), 485-495, webpage

P15.     Shaghaf Alzorba, Christian Günther and Nicolae Popovici: A special class of extended multicriteria location problems, Optimization, 64 (2015) (5), 1305-1320., doi:10.1080/02331934.2013.869810 [JCR Science Edition 2015 IF: 0,822]

P16.     Szilárd László and Adrian Viorel: Generalized monotone operators on dense sets, Numer. Funct. Anal. Optim., 36  (2015) (7), 901929, doi:10.1080/01630563.2015.1040162 [JCR Science Edition 2015 IF: 0,649]

P17.     Daniela Marian, Ioan Radu Peter and Cornel Pintea: A class of generalized monotone operators, J. Math. Anal. Appl., 421 (2015) (2), 1827–1843, doi:10.1016/j.jmaa.2014.08.017 [JCR Science Edition 2015 IF: 1,014]

P18.     Monica Bianchi, Gabor Kassay and Rita Pini: Stability results of variational systems under openness with respect to fixed sets, J. Optim. Theory Appl., 164 (2015) (1), 92-108, doi:10.1007/s10957-014-0560-4 [JCR Science Edition 2015 IF: 1,160]

P19.     Daishi Kuroiwa, Nicolae Popovici and Matteo Rocca: A characterization of cone-convexity for set-valued functions by cone-quasiconvexity, Set-Valued Var. Anal., 23 (2015) (2), 295-304,  doi:10.1007/s11228-014-0307-2 [JCR Science Edition 2015 IF: 0,973]

P20.     Ovidiu Bagdasar and Nicolae Popovici: Local maximum points of explicitly quasiconvex functions, Optim. Lett., 9 (2015) (4), 769–777,  doi:10.1007/s11590-014-0781-3, [JCR Science Edition 2015 IF: 1,019]

P21.     Gabor Kassay and Mihaela Miholca: Existence results for vector equilibrium problems given by a sum of two functions, J. Global Optim., 63 (2015) (1), 195–211, doi:10.1007/s10898-014-0264-1, [JCR Science Edition 2015 IF: 1,219]

P22.     Daishi Kuroiwa, Nicolae Popovici and Matteo Rocca: Characterizations of cone-convex vector-valued functions, Carpathian J. Math., 32 (2016) (1), 79-85, webpage, [JCR Science Edition 2015 IF: 0,610]

P23.     Nicolae Popovici: A decomposition approach to vector equilibrium problems, Ann. Oper. Res., 251 (2017) (1), 105-115, doi:10.1007/s10479-015-1861-1  [JCR Science Edition 2015 IF: 1,406]

P24.     Adela Capătă and Gabor Kassay: Characterizations of vector equilibria subject to explicit constraints, Minimax Theory and Its Applications, 1 (2016) (1), 145–161, webpage

P25.     Monica Bianchi, Gabor Kassay and Rita Pini: Linear openness of the composition of set-valued maps and applications to variational systems, Set-Valued Var. Anal., 24 (2016) (4), 581–595, doi:10.1007/s11228-015-0357-0  [JCR Science Edition 2015 IF: 0,973]

P26.     Cornel Pintea and Tiberiu Trif: The monotoncity of perturbed gradients of convex functions, J. Convex Anal., 24 (2017) (2), page numbers not yet available, webpage [JCR Science Edition 2015 IF: 0,786]

P27.     Ovidiu Bagdasar and Nicolae Popovici: Extremal properties of generalized convex vector functions, J. Nonlinear Convex Anal., accepted, [JCR Science Edition 2015 IF: 0,691]

P28.     Adela Capătă and Gabor Kassay: Existence results for strong vector equilibrium with applications, under review

P29.     Gabor Kassay, Mihaela Miholca and Nguyen The Vinh: Vector quasi-equilibrium problems for the sum of two multivalued mappings, J. Optim. Theory Appl., 169 (2016) (2), 424-442., doi: 10.1007/s10957-016-0919-9 [JCR Science Edition 2015 IF: 1,160]

P30.     Shaghaf Alzorba, Christian Günther, Nicolae Popovici and Christiane Tammer: A new algorithm for solving planar multiobjective location problems involving the Manhattan norm, European J. Oper. Res., 258 (2017) (1), 35-46, doi: 10.1016/j.ejor.2016.10.045, [JCR Science Edition 2015 IF: 2,679]

P31.     Szilárd László: Vector equilibrium problems on dense sets, J. Optim. Theory Appl., 170 (2016) (2), 437–457, 10.1007/s10957-016-0915-0 [JCR Science Edition 2015 IF: 1,160]

P32.     Ioan Radu Peter and Cornel Pintea: Necessary conditions for finite critical sets. Maps with infinite critical sets, Topol. Methods Nonlinear Anal., 47 (2016) (2), 739-749,  doi:10.12775/TMNA.2016.032 [JCR Science Edition 2015 IF: 0,717]

P33.     Juan Enrique Martinez-Legaz and Cornel Pintea: Closed convex sets of Minkowski type, J. Math. Anal. Appl., 444 (2016) (2), 1195–1202, doi:10.1016/j.jmaa.2016.06.073 [JCR Science Edition 2015 IF: 1,014]

P34.     Zsolt Darvay, Ingrid-Magdolna Papp and Petra-Renáta Takács: Complexity analysis of a full-Newton step interior-point method for linear optimization, Period. Math. Hungar., 73 (2016) (1), 27–42, http: 10.1007/s10998-016-0119-2 [JCR Science Edition 2015 IF: 0,286]

P35.     Szilárd László: Minimax results on dense sets and dense families of functionals, under review

P36.     Gabor Kassay, Tring Ngoc Hai, Nguyen The Vinh: Coupling Popov's algorithm with subgradient extragradient method for solving equilibrium problems, under review

 

 

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Conferences and seminars

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Period

Plenary/session invited talks at international conferences/workshops

Contributed talks at international conferences/workshops

Invited talks at research seminars abroad

Talks at conferences and research seminars in Romania

Total

05.10.2011 – 15.12.2011

0

0

0

0

0

16.12.2011 – 15.12.2012

2 [CS5 and CS9 in the list below]

2 [CS6 and CS8 in the list below]

6 [CS1-CS4, CS7 and CS11 in the list below]

3 [CS10, CS12 and CS13 in the list below]

13

16.12.2012– 15.12.2013

5 [CS17, CS21, CS24, CS25 and CS30 in the list below]

5 [CS26-CS29 and CS31 in the list below]

5 [CS16 and CS33-CS36 in the list below]

11 [CS14, CS15, CS18-CS20, CS22, CS23, CS32 and CS37-CS39 in the list below]

26

16.12.2013 – 31.12.2014

1 [CS45 in the list below]

5 [CS40, CS41 and CS50-CS52 in the list below]

2 [CS48 and C49 in the list below]

10 [CS42-CS44, CS46, CS47 and CS53-CS57 in the list below]

18

01.01.2015 – 31.12.2015

4 [CS63-CS65 and CS69 in the list below]

2 [CS66 and CS67 in the list below]

3 [CS58, CS59 and CS68 in the list below]

8 [CS60-C63 and CS71-CS74 in the list below]

17

01.01.2016 – 04.10.2016

-

7 [CS75, CS83-CS88 in the list below]

4 [CS76-CS78 and CS80 in the list below]

3 [CS79, CS81 and CS82 in the list below]

14

Total   

12

21

20

35

88

 

CS1.      Gábor Kassay: On a generalized proximal point method for equilibrium problems in Banach spaces, Research Seminar, Department of Mathematics, Faculty of Sciences, Cadi Ayyad University, Marrakesh, Morocco, March 22, 2012.

CS2.      Gábor Kassay: An inverse function result and some applications to sensitivity of generalized equations, Research Seminar, Department of Economics, Faculty of Economics and Social Sciences, Ibn Zohr University, Agadir, Morocco, Research Seminar, March 29, 2012.

CS3.      Nicolae Popovici:  Applications of generalized convexity in multicriteria optimization, Martin Luther University of Halle, Germany, Oberseminar Optimierung, April 23, 2012, http://www.mathematik.uni-halle.de/institute/optimierung/vario/semoptim.html.

CS4.      Nicolae Popovici: A special class of generalized convex functions with applications in vector optimization, Chemnitz University of Technology, Germany, Research Seminar Optimization and Approximation, April 25, 2012, http://www.tu-chemnitz.de/mathematik/approximation/seminars.php.

CS5.      Gábor Kassay (invited speaker): Monotone operators and closed countable sets, Workshop on “Optimization and Variational Analysis”, Universita Cattolica Del’Sacro Cuore di Milano and Universita Degli Studi di Milano Bicocca, Milano, Italy, May 10-11, 2012

CS6.      Gábor Kassay: An inverse function result and some applications to sensitivity of generalized equations, 58th Course: Variational Analysis and Applications, Erice, May 14–22, 2012.

CS7.      Nicolae Popovici: Semistrictly quasiconvex-like multicriteria optimization, University of Varese, Italy, Department of Economics, Research Seminar, June 26, 2012, http://eco.uninsubria.it/dipeco/seminari2012.htm.

CS8.      Gábor Kassay: An inverse function result and some applications to sensitivity of generalized equations, 25th European Conference on Operational Research, Vilnius, Lithuania, July 8–11, 2012, http://www.euro-2012.lt/user/_files/28/monday-program-euro25.pdf.

CS9.      Szilard Laszlo (speaker in invited session Fri.3.H 2051): Regularity conditions for the maximal monotonicity of the generalized parallel sum, The 21st International Symposium on Mathematical Programming, Berlin, Germany, August 19-24, 2012, http://ismp2012.mathopt.org/show-session?sess=110.

CS10.   Gábor Kassay: An inverse map result and some applications to sensitivity of generalized equations, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, November 1, 2012, http://www.cs.ubbcluj.ro/~grupanopt/.

CS11.   Nicolae Popovici: Decomposition of multicriteria planar location problems, University of Varese, Italy, Department of Economics, Research Seminar, November 20, 2012, http://eco.uninsubria.it/dipeco/seminari2012.htm.

CS12.   Szilárd László: Coincidence point results via variational inequalities, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, November 22, 2012, http://www.cs.ubbcluj.ro/~grupanopt/.

CS13.   Nicolae Popovici: Generalized multicriteria location problems, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, December 13, 2012, http://www.cs.ubbcluj.ro/~grupanopt/.

CS14.   Cornel Pintea: Properties of monotone operators. Applications, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, January 10, 2013, http://www.cs.ubbcluj.ro/~grupanopt/.

CS15.   Gábor Kassay: On a generalized proximal point method for solving equilibrium problems in Banach spaces, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, January 17, 2013, http://www.cs.ubbcluj.ro/~grupanopt/.

CS16.   Nicolae Popovici: Approximation of efficient points in vector optimization, University of Valle d'Aosta, Italy, Research Seminar, February 15, 2013.

CS17.   Nicolae Popovici (invited speaker): Vector optimization: a state-of-the-art survey, Workshop on Vector and Set Optimization, University of Varese, Italy, February 18, 2013.

CS18.   Mihaela Miholca (Bercheşan): On surjectivity of some classes of generalized monotone operators, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, March 14, 2013, http://www.cs.ubbcluj.ro/~grupanopt/.

CS19.   Szilard Laszlo: On some new concepts in Nonlinear Analysis, Research Seminar, Department of Mathematics, Technical University, Cluj-Napoca, March 21, 2013.

CS20.   Erika Nagy: A primal-dual splitting algorithm for solving systems of monotone inclusions, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, April 11, 2013, http://www.cs.ubbcluj.ro/~grupanopt/ .

CS21.   Gábor Kassay (invited speaker): Existence results for variational inequalities with surjectivity consequences related to generalized monotone operators, Workshop on Optimization and Variational Analysis, University of L'Aquila, May 9-10, 2013.

CS22.   Nicolae Popovici: Decomposition of vector variational inequalities, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, May 23, 2013, http://www.cs.ubbcluj.ro/~grupanopt/.

CS23.   Erika Nagy: Applications to convex minimization problems via a primal-dual splitting algorithm, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, June 13, 2013, http://www.cs.ubbcluj.ro/~grupanopt/ .

CS24.   Gábor Kassay (speaker in invited session WD-01): On a generalized proximal point method for solving equilibrum problems in Banach spaces, 11th EUROPT Workshop on Advances in Continuous Optimization, Firenze (Italy), June 26-28, 2013, http://www.europt2013.org/.

CS25.   Mihaela Miholca (Bercheşan) (speaker in invited session WE-01): Existence results for variational inequalities with surjectivity consequences related to generalized monotone operator, 11th EUROPT Workshop on Advances in Continuous Optimization, Firenze (Italy), June 26-28, 2013, http://www.europt2013.org/.

CS26.   Erika Nagy: A primal-dual splitting algorithm for solving systems of monotone inclusions, International Conference on Anatolian Communications in Nonlinear Analysis, Abant Izzet Baysal University, Bolu, Turkey, July 3-6, 2013.

CS27.   Gábor Kassay (chair of session Wed.A.25): An inverse map result and some applications to sensitivity of generalized equations, ICCOPT 2013 -The Fourth International Conference on Continuous Optimization, Lisbon, Portugal, July 27 - August 1, 2013, http://eventos.fct.unl.pt/iccopt2013.

CS28.   Mihaela Miholca (Bercheşan): Existence results for variational inequalities with surjectivity consequences related to generalized monotone operator, ICCOPT 2013 -The Fourth International Conference on Continuous Optimization, Lisbon, Portugal, July 27 - August 1, 2013, http://eventos.fct.unl.pt/iccopt2013.

CS29.   Szilárd László (chair of Session 10): Univalence results via monotonicity , 9th International Symposium on Geometric Function Theory and Applications, Işık University, Istanbul, Turkey, August 26-30, 2013, ,http://gfta.isikun.edu.tr/

CS30.   Nicolae Popovici (invited plenary speaker): On the relationship between efficiency and weak efficiency in vector optimization, XXXVII Meeting of the Italian Association for Mathematics Applied to Economic and Social Sciences (AMASES), September 5-7, 2013, Stresa, Italy, http://www.amases2013.eco.uninsubria.it/site/

CS31.   Szilárd László: Multivalued variational inequalities and coincidence point results, International Conference of Applied Mathematics, Baia Mare, Romania, September 25-28, 2013, icam.ubm.ro/index.php?icam=ICAM9

CS32.   Szilárd László: Generalized monotone operators on dense sets, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, October 10, 2013, http://www.cs.ubbcluj.ro/~grupanopt/

CS33.   Nicolae Popovici: On the relationship between efficiency and weak efficiency in vector optimization, Research Seminar, University of Derby, UK, October 21, 2013.

CS34.   Nicolae Popovici: Efficiency versus optimality in multicriteria decision making, Research Seminar, Department of Economics, University of Milan, Italy, October 23, 2013.

CS35.   Nicolae Popovici: Special classes of generalized convex vector-valued functions, Research Seminar, Department of Economics, University of Insubria, Varese, Italy, October 24, 2013, http://www.eco.uninsubria.it/site/dipartimento/ricerca/seminari-2013

CS36.   Nicolae Popovici: Multicriteria optimization problems related to location theory, Research Seminar, Department of Economics, University of Pavia, Italy, October 25, 2013.

CS37.   Nicolae Popovici: On a special class of multicriteria optimization problems, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, October 31, 2013, http://www.cs.ubbcluj.ro/~grupanopt/

CS38.   Nicolae Popovici: Explicitly quasiconvex optimization problems, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, November 7, 2013, http://www.cs.ubbcluj.ro/~grupanopt/

CS39.   Gábor Kassay: Stability results of variational systems under linear openness, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, November 21, 2013, http://www.cs.ubbcluj.ro/~grupanopt/

CS40.   Gábor Kassay: On a generalized proximal point algorithm for equilibrium problems in Banach spaces, The Third International Conference on Numerical Analysis and Optimization, 5-9 January, 2014,Sultan Qaboos University, Muscat, Sultanate of Oman, http://conference.squ.edu.om/portals/16/NAOiii%202014%20Conference%20Programme.pdf

CS41.   Mihaela Miholca (Bercheşan): Some existence results on equilibrium problems and applications, The Third International Conference on Numerical Analysis and Optimization, 5-9 January, 2014,Sultan Qaboos University, Muscat, Sultanate of Oman, http://conference.squ.edu.om/portals/16/NAOiii%202014%20Conference%20Programme.pdf

CS42.   Mihaela Miholca (Bercheşan): On vector equilibrium problems given by a sum of two functions, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, February 27, 2014, http://www.cs.ubbcluj.ro/~grupanopt/

CS43.   Nicolae Popovici: A characterization of cone-convex functions, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, March 20, 2014, http://www.cs.ubbcluj.ro/~grupanopt/

CS44.   Szilárd László: Densely defined equilibrium problems, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, May 8, 2014, http://www.cs.ubbcluj.ro/~grupanopt/

CS45.   Gábor Kassay (invited speaker): Linear openness and variational systems, Workshop on Optimization, Game Theory and Related Topics, Department of Mathematics, University of Genova, Italy, 8-9 May, 2014. 

CS46.   Cornel Pintea: A class of generalized monotone operators, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, May 15, 2014, http://www.cs.ubbcluj.ro/~grupanopt/

CS47.   Gábor Kassay: Linear openness and variational systems, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, May 22, 2014, http://www.cs.ubbcluj.ro/~grupanopt/

CS48.   Szilárd László: Self segment-dense sets, generalized monotone operators and equilibrium problems, Seminar of the Research Group on Applied Mathematics and Optimization, University of Vienna, Austria, June 12, 2014, http://plone.mat.univie.ac.at/events/2014/self-segment-dense-sets-generalized-monotone-operators-and-equilbrium-problems/view 

CS49.   Nicolae Popovici: Special classes of generalized convex vector-valued functions, Research Seminar, Department of Economics, University of Insubria, Varese, Italy, June 17, 2014, http://www.eco.uninsubria.it/site/dipartimento/ricerca/seminari/2014-2/

CS50.   Mihaela Miholca (Bercheşan): On vector equilibrium problems given by a sum of two functions, 20th Conference of the International Federation of Operational Research Societies (IFORS 2014), Barcelona, July 13-18, 2014, http://ifors2014.upc.edu/content/fa (see FA-26 Session)

CS51.   Nicolae Popovici: On certain classes of generalized convex set-valued functions, Set Optimization meets Finance (SOMF2) - International Conference on Set-Valued Variational Analysis and Optimization with Applications in Finance, September 8-12, 2014, Bruneck-Brunico, Italy, https://www.unibz.it/en/economics/research/somf2/default.html

CS52.   Szilárd László: An inertial forward-backward algorithm for minimizing the sum of two non-convex functions, 3rd  International Conference on Numerical Analysis and Approximation Theory, September 17-20, 2014, Cluj-Napoca, Romania, http://naat.math.ubbcluj.ro/index.html

CS53.   Nicolae Popovici: A decomposition approach to vector equilibrium problems, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, October 30, 2014, http://www.cs.ubbcluj.ro/~grupanopt/

CS54.   Cornel Pintea, Tiberiu Trif: On certain generalized monotone operators, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, November 6, 2014, http://www.cs.ubbcluj.ro/~grupanopt/

CS55.   Szilárd László: On injectivity of a class of monotone operators with some univalency consequences, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, November 27, 2014, http://www.cs.ubbcluj.ro/~grupanopt/

CS56.   Cornel Pintea: Operations with monotone operators and the monotonicity of the resulting operators, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, December 4, 2014, http://www.cs.ubbcluj.ro/~grupanopt/

CS57.   Gábor Kassay: Linear openness of the composition of set-valued maps and applications to variational systems, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, December 11, 2014, http://www.cs.ubbcluj.ro/~grupanopt/

CS58.   Nicolae Popovici: A decomposition approach to vector equilibrium problems, Research Seminar, Department of Economics, University of Insubria, Varese, Italy, February 9, 2015 http://www.eco.uninsubria.it/site/dipartimento/ricerca/seminari/

CS59.   Cornel Pintea: Closed convex sets of Krein-Milman type, Universitat Autňnoma de Barcelona, Spain, February 23, 2015.

CS60.   Nicolae Popovici:  A new algorithm for solving planar multiobjective location problems, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, February 26, 2015, http://www.cs.ubbcluj.ro/~grupanopt/

CS61.   Mihaela Miholca (Bercheşan): Vector quasi-equilibrium problems for the sum of two multivalued mappings, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, March 5, 2015, http://www.cs.ubbcluj.ro/~grupanopt/

CS62.   Ovidiu Bagdasar (University of Derby), Nicolae Popovici: Extremal properties of generalized convex vector-valued functions, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, April 2, 2015, http://www.cs.ubbcluj.ro/~grupanopt/

CS63.   Cornel Pintea: Closed convex sets of Minkowski type, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, April 23, 2015, http://www.cs.ubbcluj.ro/~grupanopt/

CS64.   Gábor Kassay (invited speaker): Existence results for vector equilibrium problems given by a sum of two functions, International Workshop on Evolution Problems and Optimization, Agadir, Morocco, May 4–6, 2015, poster

CS65.   Gábor Kassay (invited speaker): Vector quasi-equilibrium problems for the sum of two multivalued mappings, Workshop on Variational Analysis, Game Theory and Related Topics, Genova, Italy, May 7-8, 2015, http://www.dima.unige.it/~pusillo/workshop_2015.htm

CS66.   Gábor Kassay (invited speaker): Linear openness of the composition of set-valued maps and applications to variational systems, International Conference on Nonlinear Operators, Differential Equations and Applications (ICNODEA 2015), July 14-17, 2015, Cluj-Napoca, Romania, http://www.cs.ubbcluj.ro/~icnodeacj/index.htm

CS67.   Mihaela Miholca (Berchesan): Vector quasi-equilibrium problems for the sum of two multivalued mappings, International Conference on Nonlinear Operators, Differential Equations and Applications (ICNODEA 2015), July 14-17, 2015, Cluj-Napoca, Romania, http://www.cs.ubbcluj.ro/~icnodeacj/index.htm

CS68.   Gábor Kassay: Equilibrium problems for the sum of two multivalued mappings, MOPTA - Modeling and Optimization: Theory and Applications, 20-22 July 2015, Bethlehem PA, USA, http://coral.ie.lehigh.edu/~mopta/ , http://coral.ie.lehigh.edu/~mopta/mopta2015.pdf

CS69.   Nicolae Popovici: An embedding approach to characterize cone-convex set-valued fuctions, Research Seminar, Department of Economics, University of Insubria, Varese, Italy, September 8, 2015 http://www.eco.uninsubria.it/site/dipartimento/ricerca/seminari/

CS70.   Nicolae Popovici: (invited speaker): A decomposition approach to nonlinear multi-criteria optimization/equilibrium problems, Riemann International School of Mathematics on Nonlinear Phenomena in Mathematics and Economics - a tribute to John Forbes Nash, Jr., Varese, September 14-18, 2015 http://www.rism.it/rism4_8.html

CS71.   Nicolae Popovici: New classes of generalized convex set-valued functions defined by an embedding approach, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, October 10, 2015, http://www.cs.ubbcluj.ro/~grupanopt/

CS72.   Szilárd László: Some minimax results on dense sets and an extension of James’ Theorem, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, November 5, 2015, http://www.cs.ubbcluj.ro/~grupanopt/

CS73.   Cornel Pintea: The convex Lusternik-Schnirelmann category, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, November 12, 2015, http://www.cs.ubbcluj.ro/~grupanopt/

CS74.   Cornel Pintea: Minimal convex decompositions by maximal convex subsets, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, November 26, 2015, http://www.cs.ubbcluj.ro/~grupanopt/

CS75.   Petra-Renáta Takács: New short-step interior-point algorithm for horizontal linear complementarity problems, International Scientific Conference of Young Engineers, Cluj-Napoca, March 17-18, 2016, http://www.eme.ro/fmtu/program.htm

CS76.   Gábor Kassay: Existence results for vector equilibrium problems given by a sum of two functions, Research Seminar "Equilibrium Problems", School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Vietnam, April 5, 2016.

CS77.   Gábor Kassay: The equilibrium problem: a unified approach to optimization,minimax problems (game theory), variational inequalities and other interesting problems, Invited lecture at Vietnam Academy of Science and Technology, Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam, April 8, 2016, http://math.ac.vn/en/icalrepeat.detail/2016/04/08/2444/-/the-equilibrium-problem-a-unified-approach-to-optimization-minimax-problems-game-theory-variational-inequalities-and-other-interesting-problems.html

CS78.   Gábor Kassay: On a Generalized Proximal Point Method for Equilibrium Problems in Banach spaces. Well-Posedness for Equilibrium Problems, Research Seminar "Equilibrium Problems", School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Vietnam, April 12, 2016.

CS79.   Gábor Kassay: Research on equilibrium problems at Hanoi University of Science and Technology, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, April 21, 2016, http://www.cs.ubbcluj.ro/~grupanopt/

CS80.   Nicolae Popovici: A decomposition approach to vector optimization and equilibrium problems, Research Seminar, Department of Computing and Mathematics, University of Derby, UK, May 11, 2016.

CS81.   Gábor Kassay: Stability of equilibria via regularity of the diagonal subdifferential operators, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, May 12, 2016, http://www.cs.ubbcluj.ro/~grupanopt/

CS82.   Nicolae Popovici: Clase speciale de funcii multivoce generalizat convexe, A XX-a Conferinţă Anuală a Societăţii de Ştiinţe Matematice din România, Baia Mare, 19-22 mai 2016, http://icam.ubm.ro/

CS83.   Mihaela Miholca (Bercheşan): Existence results for vector equilibrium problems given by a sum of two functions, 28th European Conference on Operational Research, July 3-6, 2016, Poznan, Poland, http://www.euro2016.poznan.pl/

CS84.   Cornel Pintea: Monotone operators. Applications, The 15-th International Conference on Applied Mathematics and Computer Science, July 5-7, 2016, Cluj-Napoca, Romania, http://www.tucn.ro/angheluta2016/.

CS85.   Szilárd László: The minimization problem of a convex function on dense sets, The 15-th International Conference on Applied Mathematics and Computer Science, July 5-7, 2016, Cluj-Napoca, Romania, http://www.tucn.ro/angheluta2016/

CS86.   Gábor Kassay: Vector quasi-equilibrium problems for the sum of two multivalued mappings, The Fifth International Conference on Continuous Optimization, Tokyo, August 6-11, 2016, http://www.iccopt2016.tokyo/program/index.html

CS87.   Petra-Renáta Takács: New search direction-based interior-point algorithm for P*(K) horizontal linear complementarity problems over Cartesian product of symmetric cones, The Fifth International Conference on Continuous Optimization, Tokyo, August 6-11, 2016, http://www.iccopt2016.tokyo/program/index.html

CS88.   Szilárd László: Minimax Results on Dense Sets, 13čme Colloque Franco-Roumain de Mathématiques Appliquées, 25-29 August 2016, Iasi, Romania, http://www.math.uaic.ro/cfr2016/ .

 

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Ph.D. and habilitation dissertations

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PhD1.  Boglarka Burjan-Mosoni: The equilibrium problem and applications (Ph.D. Supervisor: Professor Gábor Kassay), Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania, Ph.D. Dissertation defended on March 9, 2012 (Summary available here).

PhD2.  Erika Nagy: Numerical methods for approximating zeros of operators and for solving variational inequalities with applications (Ph.D. Supervisor: Professor Gábor Kassay), Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania, Ph.D. Dissertation defended on September 26, 2013 (Summary available here).

PhD3.  Mihaela Miholca (Bercheşan): Contributions to the Theory of Equilibrium Problems and Variational Inequalities (Ph.D. Supervisor: Professor Gábor Kassay), Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania, Ph.D. Dissertation defended on June 6, 2014 (Summary available here).

Habil1. Nicolae Popovici: The role of generalized convexity in vector optimization and related variational problems, Habilitation Thesis, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania, defended on March 25, 2016 (Summary available here).

 

 

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External collaborators

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·       Lecturer Ovidiu BAGDASAR, Ph.D. (University of Derby, U.K.)

-        Research visit at Babeş-Bolyai University, Cluj-Napoca, May 15 - June 5, 2014;

-        Invited talk: On some properties and applications of Horadam sequences, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania, May 29, 2014, http://www.cs.ubbcluj.ro/~grupanopt/

-        Invited talk: Recurrent sequences and the Mathematics of beauty, Interdisciplinary Seminar, May 30, 2014,Faculty of Mathematics and Computer Science, http://www.cs.ubbcluj.ro/sesiune-de-prelegeri-invitate-pe-teme-de-cercetare-interdisciplinara-2/ 

·       Professor Monica BIANCHI, Ph.D. (Universita Cattolica del Sacro Cuore di Milano, Italy)

-        Research visit at Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, April 24-28, 2012;

-        Research visit at Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, May 2-6, 2016;

·       Professor Radu Ioan BOŢ, Ph.D. (University of Vienna, Austria)

-        Research visit at Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, March 21-24, 2016;

-        Invited talk: A primal-dual Douglas-Rachford type algorithm for nonsmooth convex optimization problems with complex structures, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania, March 24, 2016, http://www.cs.ubbcluj.ro/~grupanopt/

 

·       Professor Marco CASTELLANI, Ph.D. (Universita degli Studi dell'Aquila, Italy)

-        Research visit at Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, October 20-27, 2012;

-        Invited talk: Existence of solutions and stability for equilibrium problems, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Cluj-Napoca, Romania, October 25, 2012, http://www.cs.ubbcluj.ro/~grupanopt/ ;

-        Research visit at Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, June 10-15, 2016;

 

·       Christian GÜNTHER, Ph.D. student (Martin Luther University, Halle-Wittenberg, Germany);

-        Invited talk: Relationships between constrained and unconstrained multi-objective optimization, Seminar of the Research Group on Analysis and Optimization, Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania, April 28, 2016, http://www.cs.ubbcluj.ro/~grupanopt/

·       Professor Boris S. MORDUKHOVICH, Ph.D. (Wayne State University, Detroit, USA)

-        Research visit at Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, June 8-13, 2013;

-        Doctor Honoris Causa speech, Babeş-Bolyai University, Cluj-Napoca, June 12, 2013, (English and Romanian versions are available here)

 

·       Professor Rita PINI, Ph.D. (Universita degli Studi di Milano Bicocca, Italy)

-        Research visit at Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, April 24-28, 2012;

-        Research visit at Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, May 2-6, 2016.

 

 

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Annual scientific reports

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The Scientific Report No.1 (on the period of 05.10.2011 – 15.12.2011) is available here

The Scientific Report No.2 (on the period of 16.12.2011 – 15.12.2012) is available here

The Scientific Report No.3 (on the period of 16.12.2012 – 15.12.2013) is available here

The Scientific Report No.4 (on the period of 16.12.2013 – 31.12.2014) is available here

The Scientific Report No.5 (on the period of 01.01.2015 – 31.12.2015) is available here

The Scientific Report No.6 (on the period of 01.01.2016 – 04.10.2016) is available here

 

 

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Updated by Nicolae Popovici on April 3, 2017