On the second-order sufficient optimality condition in nonconvex multiobjective optimization problems

The study of second-order optimality conditions is one of the most important topics in optimization theory and attracting the attention and interest of many authors. In this paper, we introduce a novel solution concept called “essential local efficient solutions of second-order” for nonconvex constrained multiobjective optimization problems. We then show that the new solution concept is stronger than the quadratic growth condition and under a mild constraint qualification, these solution concepts are equivalent. By using the second subderivative, we derive a sufficient optimality condition for a feasible solution to become an essential local efficient solution of second-order for the considered problem. Examples are provided to illustrate the obtained results.