Lagrange multiplier characterizations of solution sets of constrained pseudolinear optimization problems

In this article, we study the minimization of a pseudolinear (i.e. pseudoconvex and pseudoconcave) function over a closed convex set subject to linear constraints. Various dual characterizations of the solution set of the minimization problem are given. As a consequence, several characterizations of the solution sets of linear fractional programs as well as linear fractional multi-objective constrained problems are given. Numerical examples are also given.

[1]  Didier Aussel.  Subdifferential Properties of Quasiconvex and Pseudoconvex Functions: Unified Approach , 1998 .

[2]  Eng Ung Choo,et al.  Pseudolinearity and efficiency , 1984, Math. Program..

[3]  A. M. Geoffrion.  Proper efficiency and the theory of vector maximization , 1968 .

[4]  O. Mangasarian.  A simple characterization of solution sets of convex programs , 1988 .

[5]  Olvi L. Mangasarian,et al.  Nonlinear Programming , 1969 .

[6]  Siegfried Schaible,et al.  An Extension of Pseudolinear Functions and Variational Inequality Problems , 1999 .

[7]  James V. Burke,et al.  Characterization of solution sets of convex programs , 1991, Oper. Res. Lett..

[8]  Kenneth O. Kortanek,et al.  Pseudo-Concave Programming and Lagrange Regularity , 1967, Oper. Res..

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

[10]  Vaithilingam Jeyakumar,et al.  Lagrange Multiplier Conditions Characterizing the Optimal Solution Sets of Cone-Constrained Convex Programs , 2004 .

[11]  S. Komlósi.  First and second order characterizations of pseudolinear functions , 1993 .

[12]  Vaithilingam Jeyakumar.  Infinite-dimensional convex programming with applications to constrained approximation , 1992 .

[13]  Xiaoqi Yang,et al.  Convex composite multi-objective nonsmooth programming , 1993, Math. Program..

[14]  Vaithilingam Jeyakumar,et al.  Characterizations of solution sets of convex vector minimization problems , 2006, Eur. J. Oper. Res..

[15]  Xiaoqi Yang.  Vector Variational Inequality and Vector Pseudolinear Optimization , 1997 .

[16]  J. Penot,et al.  Characterization of Solution Sets of Quasiconvex Programs , 2003 .

[17]  Tamás Rapcsák,et al.  On pseudolinear functions , 1991 .

[18]  Henry Wolkowicz,et al.  Generalizations of Slater's constraint qualification for infinite convex programs , 1992, Math. Program..

[19]  Xiaoqi Yang,et al.  On characterizing the solution sets of pseudolinear programs , 1995 .