An l1 Exact Exponential Penalty E-Function Method for E-Differentiable Vector Optimization Problems Under E-Exponential Type Invexity

Abstract

In this paper, a new concept of generalised convexity and a new class of exact exponential penalty method, namely the concept of $\left(p,r\right)$-E-invexity and $l_1$ exact exponential penalty E-function method, respectively are introduced for (not necessarily) differentiable vector optimization problem in which functions are E-differentiable. The conditions governing the equivalence between sets of (weak) efficient solutions of the original constrained E-differentiable vector optimization problem and of its associated unconstrained exponential penalised vector optimization problem are studied. Examples are given to illustrate the obtained results.