Local Uniqueness of Solutions to Ky Fan Vector Inequalities using Approximations as Derivatives
- 321 Downloads
We establish sufficient conditions for the local uniqueness of solutions to Ky Fan vector strong and weak inequalities. By using approximations as generalized derivatives, our results are valid even in cases where the maps involved in the problems suffer infinite discontinuity at the considered point. Corollaries and examples show that the results extend and improve existing ones in the literature.
KeywordsLocal uniqueness Ky Fan vector strong and weak inequalities Approximations
This work was supported by the National Foundation for Science and Technology Development of Vietnam. The final work on the paper of the first author was carried out during his stay at the Vietnam Institute for Advanced Study in Mathematics (VIASM) as a Visiting Professor. The authors would like to thank the Handling Editor and Anonymous Referees for their valuable remarks and suggestions, and for VIASM for the hospitality.
- 1.Fan, K.: A minimax inequality and applications. In: Shisha, O. (ed.) Inequality III, pp. 103–113. Academic Press, New York (1972) Google Scholar
- 18.Khanh, P.Q., Tung, N.M.: Optimality and duality for nonsmooth set-valued vector equilibrium problems. Submitted for publication Google Scholar
- 21.Khanh, P.Q., Tung, L.T.: First and second-order optimality conditions using approximations for vector equilibrium problems with constraints. Submitted for publication Google Scholar
- 32.Khanh, P.Q., Tuan, N.D.: Optimality conditions without continuity in multivalued optimization using approximations as generalized derivatives. In: Mishra, S.K. (ed.) Recent Contributions in Nonconvex Optimization, pp. 47–61. Springer, Berlin (2011) Google Scholar