An equivalent fractional optimization problem under invexity conditions for solving fractional vector variational-like inequality problems to portfolio optimization in finance

Abstract

This paper introduces and investigates new classes of weak fractional vector variational-like inequalities and fractional vector variational-like inequalities. We establish an equivalence between the efficient solutions of fractional optimization problems and the solutions of introduced inequalities using a parametric approach under generalized invexity assumptions. By applying the KKM Lemma, we prove the existence of solutions for a fractional vector variational-like inequality problem. We also illustrate the derived results with examples. Additionally, we consider an application-based problem in portfolio allocation to validate our findings.