Strong Vector Minimization and Duality
B. D. Craven · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1980
Abstract A constrained minimum of a vector valued function is defined, in terms of an ordering cone. The definition chosen leads to a vector analog of the Kuhn‐Tucker theorem, and to a duality theorem where the dual problem has a vector valued objective function, and weak duality is defined by appropriate cone orderings. Also proved are a vector valued converse duality theorem, and a vector quasiduality theorem which does not require convexity. The results are related to perturbations of the objective function in a minimization problem.