Higher-order KKT optimality conditions through contingent derivatives for constrained nonsmooth vector equilibrium problems
Tran Van Su, Đinh Diệu Hằng · Journal of Computational and Applied Mathematics · 2024
In this paper, we deal with some higher-order optimality conditions for local strict efficient solutions to a nonsmooth vector equilibrium problem with set, cone and equality constraints. For this aim, the concept of m − stable and m − steady functions ( m ≥ 2 and integer) for single-valued functions and some constraint qualifications of higher order in terms of contingent derivatives are proposed accordingly. We analyze the sum calculus rule of m th-order adjacent set, m th-order interior set, asymptotic m th-order tangent cone and asymptotic m th-order adjacent cone. Subsequently, we employ the obtained calculus rules to treat KKT necessary and sufficient optimality conditions of higher order in terms of contingent derivatives for the m th-order (local) strict efficient solutions to such problem. Simultaneously, we employ these rules to study KKT higher-order optimality conditions for such efficient solutions for a nonsmooth vector optimization problem with constraints. Some illustrative examples are provided to demonstrate the main results of the literature.