Reducing the complexity of equilibrium problems and applications to best approximation problems

Valerian Alin Fodor, Nicolae Popovici

Abstract


We consider the scalar equilibrium problems governed by a bifunction in a finite-dimensional framework and we characterize the solutions by means of extreme or exposed points.

Keywords


Extreme points; exposed points; equilibrium points

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References


Minkowski, H., Theorie der konvexen Körper, insbesondere Begründung ihres Oberflächenbegriffs in Gesammelte Abhandlungen, Vol. 2, B. G. Teubner, Leipzig and Berlin, 1911, 131-229.

Webster, R., Convexity, Oxford University Press, New York, NY, 1994.

Breckner, B.E., Popovici, N., Convexity and Optimization: An Introduction, EFES, Cluj-Napoca, 2006.

Martínez-Legaz, J.E., Pintea, C., Closed convex sets with an open or closed Gauss range, Math Program., 189 (2021), 433-454.

Muu, LêD., Oettli, W., Convergence of an adaptive penalty scheme for finding constrained equilibria, Nonlinear Anal., 18 (1992), 1159-1166.

Kassay, G, Rădulescu, V.D., Equilibrium Problems and Applications. Mathematics in Science and Engineering, Elsevier/Academic Press, London, 2019.

Martínez-Legaz J.E, Pintea C., Closed convex sets of Minkowski type, J. Math. Anal. Appl., 444 (2016), 1195-1202.




DOI: http://dx.doi.org/10.24193/subbmath.2023.3.13

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