Higher-order optimality conditions for nonregular multiobjective problem

Abstract

In this paper, we present necessary and sufficient optimality conditions for multiobjective problems with equality and inequality constraints defined in Banach spaces. We focus on the nonregular case when the linear independence qualification or Mangasarian-Fromovitz constraint qualification are not satisfied at the solution of the multiobjective problem. For this case, we present new generalized p-order necessary optimality conditions of Karush–Kuhn–Tucker type. The conditions subsume the classical conditions and give new and nontrivial conditions for the nonregular case. Our results were obtained from the theory of p-regularity, introduced by Brezhneva and Tret’yakov (SIAM J Control Optim 42:729-745, 2003). Some examples are presented to illustrate the results.