Optimality Conditions Associated with New Controlled Extremization Models

Applying a parametric approach, in this paper we studied a new class of multidimensional extremization models with data uncertainty. Concretely, first, we derived the robust conditions of necessary optimality. Thereafter, we established robust sufficient optimality conditions by employing the various forms of convexity of the considered functionals. In addition, we formulated an illustrative example to validate the theoretical results.