Second-order necessary efficiency conditions for nonsmooth vector equilibrium problems
- 123 Downloads
This paper presents primal and dual second-order Fritz John necessary conditions for weak efficiency of nonsmooth vector equilibrium problems involving inequality, equality and set constraints in terms of the Páles–Zeidan second-order directional derivatives. Dual second-order Karush–Kuhn–Tucker necessary conditions for weak efficiency are established under suitable second-order constraint qualifications.
KeywordsPrimal and dual second-order necessary efficiency conditions Páles–Zeidan second-order directional derivatives First and second-order tangent vectors Second-order constraint qualifications
Mathematics Subject Classification90C46 90C29
The author is grateful to the referees for their valuable comments and suggestions which improve the paper. This research was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2017.301
- 3.Blum, E., Oettli, W.: From optimization and variational inequalit ies to equilibrium problems. Math. Stud. 63, 127–149 (1994)Google Scholar
- 9.Giannessi, F., Mastroeni, G., Pellegrini, L.: On the theory of vector optimization and variational inequalities, image space analysis and separation. In: Giannessi, F. (ed.) Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, pp. 153–215. Kluwer, Dordrecht (2000)CrossRefGoogle Scholar