On G-invexity-type nonlinear programming problems

Abstract

In this paper, we introduce the concepts of KT-G-invexity and WD$-G-invexity for the considered differentiable optimization problem with inequality constraints. Using KT-G-invexity notion, we prove new necessary and sufficient optimality conditions for a new class of such nonconvex differentiable optimization problems. Further, the so-called G-Wolfe dual problem is defined for the considered extremum problem with inequality constraints. Under WD-G-invexity assumption, the necessary and sufficient conditions for weak duality between the primal optimization problem and its G-Wolfe dual problem are also established.

Keywords

• mathematical programming
• KT-G-invexity
• WD-G-invexity
• G-Karush-Kuhn-Tucker point
• G-Wolfe dual problem