On multiobjective optimization problems involving higher order strong convexity using directional convexificators

In this paper, we introduce the notion of strong convexity of higher order along continuity directions based on strong convexity of higher order by Lin and Fukushima (Some Exact Penalty Results for Nonlinear Programs and Mathematical Programs with Equilibrium Constraints. J Optim Theory Appl. 2003;118:67–80) and convexity along continuity directions by Dempe and Pilecka (Necessary optimality conditions for optimistic bilevel programming problems using set-valued programming. J Glob Optim. 2015;61:769–788). We characterize strong convexity of higher order along continuity directions of a function using the monotonicity of the associated directional convexificators. We have also studied multiobjective optimization problems involving strongly convex functions of higher order along continuity directions. We use vector variational inequalities of higher order in terms of directional convexificators to identify strict minimizers and semi-strict minimizers for the multiobjective optimization problems.