Necessary and sufficient optimality conditions and a new approach for solving the smooth multiobjective fractional continuous-time programming problem

Abstract

In this paper, the multi-objective fractional continuous-time programming problem with in equality constraints is considered. We investigate the optimality conditions for this problem under weaker assumptions than in [34], Necessary optimality conditions are obtained under a suitable constraint qualification and a certain regularity condition without convexity/concavity assumptions. It is important to highlight that the assumptions of convexity/concavity on objective and constraint functions in [34] are stronger than the assumptions in this paper. Here, there are no assumptions of convexity/concavity for deriving necessary optimality conditions. Also, the constraint qualifications and a certain regularity condition presented in this paper are much less restrictive and easier to verify than the constraint qualifications given in [34]. This means that the necessary optimality conditions, set in this paper, are obtained under the weakest possible assumptions that are known to date. The already achieved results in the area of multi-objective fractional continuous-time programming are improved and more generalized in this paper. Also, we provide several examples to illustrate our results.