Sequential Optimality Conditions for Fractional Optimization with Applications to Vector Optimization

Abstract

In this paper, in the absence of any constraint qualifications, a sequential Lagrange multiplier rule condition characterizing optimality for a fractional optimization problem is obtained in terms of the $$\varepsilon $$ ? -subdifferentials of the functions involved at the minimizer. The significance of this result is that it yields the standard Lagrange multiplier rule condition for the fractional optimization problem under a simple closedness condition that is much weaker than the well-known constraint qualifications. A sequential condition characterizing optimality involving only subdifferentials at nearby points to the minimizer is also investigated. As applications, the proposed approach is applied to investigate sequential optimality conditions for vector fractional optimization problems.