Lagrange multiplier characterizations of solution sets of constrained pseudolinear optimization problems

Abstract

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.

Keywords:

• Pseudolinear functions
• Pseudolinear programs
• Linear fractional programs
• Linear fractional vector programs
• Efficient minimizers
• Properly efficient minimizers

Keywords:

• Mathematics Subject Classifications 2000: 90C26
• 90C29
• 90C30
• 65Kxx

Acknowledgements

The authors are grateful to the referees for their valuable comments and constructive suggestions which have contributed to the final preparation of the article.

The third author (G.M.L.) was supported by the Brain Korea 21 Project in 2003.