Abstract
In this paper, we first give a vector-valued version of Brézis and Browder’s scalar general principle. We then apply the vector-valued general principle to study a vector Ekeland’s variational principle in a F-type topological space, which unifies and improves the corresponding vector-valued Ekeland’s variational results in complete metric space.
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Brézis H, Browder FE (1976) A general principle on ordered sets in nonlinear functional analysis. Adv Math 21: 355–364
Fang JX (1996) The variational principle and fixed point theorems in certain topological spaces. J Math Anal Appl 202: 398–412
Hamel A (2001) Equivalents to Ekeland’s variational principle in F-type topological spaces. Report of the Institute of Optimization and Stochastic, Martin-Luther-University Halle-Wittenberg, Department of Mathematics and Computer Science
Isac G (1996) The Ekeland principle and the Pareto ε-efficiency. In: Tamig M (eds) Multiobjective Programming and Goal Programming, theory and applications. Lecture notes in economics and mathematical systems, vol 432. Springer, Berlin, pp 148–163
Li SJ, Yang XQ, Chen GY (2000) Vector Ekeland variational principle. In: Giannessi F (eds) Vector varational inequalities and vector equilibria. Nonconvex optimization and its applications, vol 38. Kluwer, Dordrecht, pp 321–333
Tammer C (1992) A generalization of Ekeland’s variational principle. Optimization 25: 129–141
Zhu J, Li SJ (2007) Generalization of ordering principles and applications. J Optim Theory Appls 132(3): 493–507
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This project was partially supported by the Research Grants Council of Hong Kong (BG771) and National Natural Science Foundation of China (70501015, 70401006).
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Chen, GY., Yang, X.Q. & Yu, H. Vector Ekeland’s variational principle in an F-type topological space. Math Meth Oper Res 67, 471–478 (2008). https://doi.org/10.1007/s00186-007-0205-6
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DOI: https://doi.org/10.1007/s00186-007-0205-6