On the algebraic criteria for local Pareto optima. II
Yieh Hei Wan · Transactions of the American Mathematical Society · 1978
Constrained vector optimization problems in the large are studied in this paper. Fixing any constraints so that the feasible set is a manifold with corners, we prove that the set of local Pareto optima for typical vector-valued functions admit Whitney prestratifications. Furthermore, these prestratifications persist under small perturbation of vector-valued functions. The main tools used here are a variant of Thom’s transversality theorem and the stratification theory of semialgebraic sets.