Role of α-Pseudo-Univex Functions in Vector Variational-Like Inequality Problems

In this paper, we introduce a new class of generalized convex function, namely, α-pseudo-univex function, by combining the concepts of pseudo-univex and α-invex functions. Further, we establish some relationships between vector variational-like inequality problems and vector optimization problems under the assumptions of α-pseudo-univex functions. Results obtained in this paper present a refinement and improvement of previously known results.

[1]  B. Mond,et al.  Pre-invex functions in multiple objective optimization , 1988 .

[2]  Norma G. Rueda,et al.  Optimality and duality with generalized convexity , 1995 .

[3]  G. Mastroeni Some remarks on the role of generalized convexity in the theory of variational inequalities , 1999 .

[4]  Xiaoqi Yang,et al.  Generalized convex functions and vector variational inequalities , 1993 .

[5]  M. Noor,et al.  ON GENERALIZED PREINVEX FUNCTIONS AND MONOTONICITIES , 2004 .

[6]  C. R. Bector,et al.  Univex sets, functions and univex nonlinear programming , 1994 .

[7]  K. K. Lai,et al.  Nondifferentiable multiobjective programming under generalized d , 2005, Eur. J. Oper. Res..

[8]  M. A. Hanson On sufficiency of the Kuhn-Tucker conditions , 1981 .

[9]  Xiaoqi Yang,et al.  A class of nonconvex functions and pre-variational inequalities , 1992 .

[10]  Xiaoqi Yang,et al.  On Some Equivalent Conditions of Vector Variational Inequalities , 2000 .

[11]  Shashi Kant Mishra,et al.  Optimality and Duality with Generalized Semi — Univexity , 2000 .

[12]  Xiaoqi Yang,et al.  On Vector Variational Inequalities: Application to Vector Equilibria , 1997 .

[13]  Antonio Rufián-Lizana,et al.  Relationships between vector variational-like inequality and optimization problems , 2004, Eur. J. Oper. Res..

[14]  M. Noor On Hadamard integral inequalities involving two log-preinvex functions. , 2007 .

[15]  Shashi Kant Mishra On Multiple-Objective Optimization with Generalized Univexity , 1998 .

[16]  R. Osuna-Gómez,et al.  Invex Functions and Generalized Convexity in Multiobjective Programming , 1998 .

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