Non convex optimization problems on weakly compact subsets of Banach spaces
Abstract
Not available.Downloads
References
Asplund, Edgar, Farthest points in reflexive locally uniformly rotund Banach spaces. Israel J. Math. 4 1966 213-216, MR0206662, https://doi.org/10.1007/BF02771633.
Baranger, J., Existence de solutions pour des problèmes d'optimisation non convexe. (French) J. Math. Pures Appl. (9) 52 (1973), 377-405 (1974), MR0380360.
Baranger, J., Temam, R., Nonconvex optimization problems depending on a parameter. SIAM J. Control 13 (1975), 146-152, MR0430901.
Barbu, V., Precupanu, Th., Convexity and optimization in Banach spaces. Revised edition. Translated from the Romanian. Editura Academiei, Bucharest; Sijthoff & Noordhoff International Publishers, Alphen aan den Rijn, 1978. xi+316 pp. ISBN: 90-286-0018-3, MR0513634.
Bidaut, M. F. Existence theorems for usual and approximate solutions of optimal control problems. Existence theory in the calculus of variations and optimal control. J. Optimization Theory Appl. 15 (1975), 393-411, MR0415449.
Brézis, Haïm, Strauss, Walter A., Semi-linear second-order elliptic equations in L1. J. Math. Soc. Japan 25 (1973), 565-590, MR0336050.
Cobzaş, Ş., Antiproximinal sets in some Banach spaces. Papers presented at the Fifth Balkan Mathematical Congress (Belgrade, 1974). Math. Balkanica 4 (1974), 79-82, MR0377381.
Day, Mahlon M., Strict convexity and smoothness of normed spaces. Trans. Amer. Math. Soc. 78, (1955). 516-528, MR0067351, https://doi.org/10.1090/S0002-9947-1955-0067351-1
Edelstein, Michael, Farthest points of sets in uniformly convex Banach spaces. Israel J. Math. 4 1966 171-176, MR0203426, https://doi.org/10.1007/BF02760075.
Edelstein, M., On nearest points of sets in uniformly convex Banach spaces. J. London Math. Soc. 43 1968 375-377, MR0226364, https://doi.org/10.1112/jlms/s1-43.1.375
Ekeland, Ivar, Lebourg, Gérard, Generic Fréchet-differentiability and perturbed optimization problems in Banach spaces. Trans. Amer. Math. Soc. 224 (1976), no. 2, 193-216 (1977), MR0431253, https://doi.org/10.2307/1997470
Lau, Ka Sing Farthest points in weakly compact sets. Israel J. Math. 22 (1975), no. 2, 168-174, MR0394126, https://doi.org/10.1007/BF02760164
Lau, Ka Sing, Almost Chebyshev subsets in reflexive Banach spaces. Indiana Univ. Math. J. 27 (1978), no. 5, 791-795, MR0510772, https://www.jstor.org/stable/24892301
Lions, J.-L., Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles. (French) Avant propos de P. Lelong Dunod, Paris; Gauthier-Villars, Paris 1968 xiii+426 pp., MR0244606.
Stečkin, S. B., Approximation properties of sets in normed linear spaces. (Russian) Rev. Math. Pures Appl. 8 1963 5-18, MR0155168.
Troyanski, S. L., On locally uniformly convex and differentiable norms in certain non-separable Banach spaces. Studia Math. 37 (1970/71), 173-180, MR0306873.
Downloads
Published
Issue
Section
License
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
