The gap function for optimization problems in Banach spaces

Abstract In this paper some properties of the gap function for multiple-objective optimization problems in Banach spaces are established.

[1]  M. Patriksson Nonlinear Programming and Variational Inequality Problems: A Unified Approach , 1998 .

[2]  R. Boţ,et al.  Conjugate duality in vector optimization and some applications to the vector variational inequality , 2007 .

[3]  Shashi Kant Mishra,et al.  Vector variational-like inequalities and non-smooth vector optimization problems , 2006 .

[4]  S. R. Mohan,et al.  On Invex Sets and Preinvex Functions , 1995 .

[5]  S. Itoh,et al.  Variational inequalities and complementarity problems , 1978 .

[6]  Tadeusz Antczak,et al.  Mean value in invexity analysis , 2005 .

[7]  Majid Soleimani-damaneh,et al.  Multiple-objective programs in Banach spaces: Sufficiency for (proper) optimality , 2007 .

[8]  G. Giorgi,et al.  The Notion of Invexity in Vector Optimization: Smooth and Nonsmooth Case , 1998 .

[9]  B. Craven Invex functions and constrained local minima , 1981, Bulletin of the Australian Mathematical Society.

[10]  P. Pardalos,et al.  Equilibrium problems : nonsmooth optimization and variational inequality models , 2004 .

[11]  S. Y. Wang,et al.  Duality in Vector Optimization in Banach Spaces with Generalized Convexity , 2004, J. Glob. Optim..

[12]  X. Q. Yang,et al.  The gap function of a convex multicriteria optimization problem , 1998, Eur. J. Oper. Res..

[13]  M. A. Rojas-Medar,et al.  Optimally Conditions for Pareto Nonsmooth Nonconvex Programming in Banach Spaces , 1999 .

[14]  F. Clarke Optimization And Nonsmooth Analysis , 1983 .

[15]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[16]  M. Minami Weak Pareto-optimal necessary conditions in a nondifferentiable multiobjective program on a Banach space , 1983 .

[17]  M. Rojas-Medar,et al.  Preinvex functions and weak efficient solutions for some vectorial optimization problem in Banach spaces , 2004 .

[18]  A. Auslender Optimisation : méthodes numériques , 1976 .

[19]  Donald W. Hearn,et al.  The gap function of a convex program , 1982, Operations Research Letters.

[20]  L. Thibault,et al.  Lagrange multiplers for pareto nonsmooth programming problems in banach spaces , 1992 .

[21]  Muhammad Aslam Noor,et al.  On vector variational-like inequality problems , 2005 .

[22]  Brahim Aghezzaf,et al.  Generalized Invexity and Duality in Multiobjective Programming Problems , 2000, J. Glob. Optim..

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

[24]  Adi Ben-Israel,et al.  What is invexity? , 1986, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.