论文信息 - On Vector Equilibrium and Vector Variational Inequality Problems

On Vector Equilibrium and Vector Variational Inequality Problems

The scalar equilibrium problem has numerous applications in Mathematical Physics, Economics and Game Theory and includes optimization and variational inequality problems. The vector equilibrium problem (VEP) is a generalization of the scalar one and it is also extensively investigated. In this work we consider relationships between VEP and other general vector problems. First we investigate ways of transforming VEP into a vector variational inequality problem under a K-space setting and obtain the relationships between monotonicity type properties of the corresponding functions. Next, we present a new gap function for VEP which allows one to reduce VEP to a vector optimization problem with single-valued function. We also consider applications of these results to vector saddle point and inverse vector optimization problems.

Igor V. Konnov

[1] W. Oettli. A remark on vector-valued equilibria and generalized monotonicity , 1997 .

[2] Xiaoqi Yang. Vector variational inequality and its duality , 1993 .

[3] S. Schaible,et al. Vector Equilibrium Problems with Generalized Monotone Bifunctions , 1997 .

[4] F. Browder,et al. On the unification of the calculus of variations and the theory of monotone nonlinear operators in banach spaces. , 1966, Proceedings of the National Academy of Sciences of the United States of America.

[5] Nicolas Hadjisavvas,et al. Quasimonotonicity and Pseudomonotonicity in Variational Inequalities and Equilibrium Problems , 1998 .

[6] Bruce D. Craven,et al. A vector variational inequality and optimization over an efficient set , 1990, ZOR Methods Model. Oper. Res..

[7] J. G. Wendel,et al. ORDERED VECTOR SPACES , 1952 .

[8] Jen-Chih Yao,et al. Existence of a Solution and Variational Principles for Vector Equilibrium Problems , 2001 .

[9] Xiaoqi Yang,et al. On Gap Functions for Vector Variational Inequalities , 2000 .

[10] Abul Hasan Siddiqi,et al. Functional Analysis with Current Applications in Science, Technology and Industry , 1997 .

[11] F. Giannessi. Vector Variational Inequalities and Vector Equilibria , 2000 .

[12] Jen-Chih Yao,et al. Existence of solutions for generalized vector equilibrium problems , 1999 .

[13] Jen-Chih Yao,et al. On the Generalized Vector Variational Inequality Problem , 1997 .