Gap Functions for Vector Equilibrium Problems via Conjugate Duality
This chapter deals with the so-called perturbation approach in the conjugate duality for vector optimization on the basis of weak orderings. As applications, we investigate some new set-valued gap functions for vector equilibrium problems.
Keywordsconjugate duality perturbation approach vector equilibrium problems set-valued gap functions
The research of the first author has been supported partially by Deutsche Forschungsgemeinschaft. The authors are grateful to Dr. Radu Ioan Boţ for valuable discussions.
- 6.Blum, E., Oettli, W. Variational principles for equilibrium problems. In: J. Guddat, (Ed.) et al., Parametric Optimization and Related Topics. III. Proceedings of the 3rd conference held in Güstrow, Germany, Frankfurt am Main: Peter Lang Verlag. Approximation Optimization. 3, 79–88 (1993)Google Scholar
- 9.Sawaragi, Y., Nakayama, H., Tanino, T. Theory of Multiobjective Optimization, Mathematics in Science and Engineering, (Vol. 176), Academic, Orlando etc. (1985)Google Scholar
- 15.Wanka, G., Boţ, R.I. On the relations between different dual problems in convex mathematical programming. In: P. Chamoni, R. Leisten, A. Martin, J. Minnemann, H. Stadler (Eds.), Operations Research Proceedings 2001 (pp. 255–262), Springer, Berlin, (2002)Google Scholar