Non convex optimization problems on weakly compact subsets of Banach spaces

Ş. Cobzaş

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Ş. Cobzaş "Tiberiu Popoviciu", Institute of Numerical Analysis, Romanian Academy, Romania

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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.