Saddle point criteria and Wolfe duality in nonsmooth (Φ, ρ)-invex vector optimization problems with inequality and equality constraints

Abstract

In this paper, saddle point criteria and Wolfe duality theorems are established for a new class of nondifferentiable vector optimization problems with inequality and equality constraints. The results are proved under nondifferentiable (Φ, ρ)-invexity and related scalar and vector-valued Lagrangians defined for the considered nonsmooth multiobjective programming problem. It turns out that the results are established for such vector optimization problems in which not all functions constituting a vector optimization problem possess the fundamental property of invexity and the most of generalized invexity notions previously defined in the literature.

Keywords:

• nonsmooth vector optimization
• Clarke subdifferential
• (Φ, ρ)-invexity
• saddle point
• Lagrange function
• Wolfe duality

2000 AMS Subject Classifications::

• 90C29
• 90C30
• 90C26
• 49J52