Reducing the complexity of equilibrium problems and applications to best approximation problems
DOI:
https://doi.org/10.24193/subbmath.2023.3.13Keywords:
Extreme points, exposed points, equilibrium points.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.
Mathematics Subject Classification (2010): 52A20, 41A50, 46N10, 90C33.
References
Breckner, B.E., Popovici, N., Convexity and Optimization: An Introduction, EFES, Cluj- Napoca, 2006.
Kassay, G., Rădulescu, V.D., Equilibrium Problems and Applications. Mathematics in Science and Engineering, Elsevier/Academic Press, London, 2019.
Martinez-Legaz, J.E, Pintea, C., Closed convex sets of Minkowski type, J. Math. Anal. Appl., 444(2016), 1195-1202.
Martinez-Legaz, J.E., Pintea, C., Closed convex sets with an open or closed Gauss range, Math. Program., 189(2021), 433-454.
Minkowski, H., Theorie der konvexen Körper, insbesondere Begründung ihres Oberflächenbegriffs, in Gesammelte Abhandlungen, Vol. 2, B.G. Teubner, Leipzig and Berlin, 1911, 131-229.
Muu, L.D., Oettli, W., Convergence of an adaptive penalty scheme for finding constrained equilibria, Nonlinear Anal., 18(1992), 1159-1166.
Webster, R., Convexity, Oxford University Press, New York, NY, 1994.
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