Invex programming problems with equality and inequality constraints

Abstract

The class of functions is known as invex function (invariant convex) in the literature and the name derives from the fact that the convex like property of such functions remains invariant under all diffeomorphisms of $R^n$ into $R^n.$ A noteworthy result here is that the class of invex functions is precisely the class of differentiable functions whose stationary points are global minimizers. We revisit some of the important results obtained by Hanson and Martin and extend them to constrained minimization problems with equality constraints in addition to inequality constraints. We address some conditions by which a function is invex. We propose a result to solve pseudo-invex programming problem with the help of an equivalent programming problem.