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Some variants of the Ekeland variational principle for a set-valued map. (English) Zbl 1064.49018
Summary: This paper deals with the Ekeland variational principle (EVP) for a set-valued map F with values in a vector space E. Using the concept of cone extension and the Mordukhovich coderivative, we formulate some variants of the EVP for F under various continuity assumptions. We investigate also the stability of a set-valued EVP. Our approach is motivated by the set approach proposed by Kuroiwa for minimizing set-valued maps.

MSC:
49J53Set-valued and variational analysis
49J52Nonsmooth analysis (other weak concepts of optimality)
References:
[1] · Zbl 0286.49015 · doi:10.1016/0022-247X(74)90025-0
[2] · Zbl 0779.49015 · doi:10.1287/moor.18.1.173
[3] · Zbl 0936.49012 · doi:10.1007/s001860050020
[4] · Zbl 1042.90036 · doi:10.1023/A:1004663208905
[5] · Zbl 1053.49019 · doi:10.1006/jmaa.2000.7357
[6] · Zbl 1029.49020 · doi:10.1080/02331930211982
[7]Kuroiwa, D., Some Duality Theorems for Set-Valued Optimization with Natural Criteria, Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis, World Scientific, Singapore, Republic of Singapore, pp. 221-228, 2001.
[8] · Zbl 1042.49524 · doi:10.1016/S0362-546X(01)00274-7
[9] · Zbl 0595.90085 · doi:10.1007/BF00940198
[10]
[11]
[12] · Zbl 0866.90103 · doi:10.1007/BF02192246
[13]Fan, K., A Minimax Inequality and Applications, Inequalities III, Proceeding of the 3rd Symposium Dedicated to the Memory of Theodore S. Motzkin, University of California, Los Angeles, California 1969; Academic Press, New York, NY, pp. 103-113, 1972.
[14]
[15]
[16]
[17] · Zbl 0881.49009 · doi:10.1090/S0002-9947-96-01543-7
[18]