Lipschitz and differentiable dependence of solutions on a parameter in a scalarization method
Alicia Sterna-Karwat · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1987
Abstract This paper is concerned with a vector optimization problem set in a normed space where optimality is defined through a convex cone. The vector problem can be solved using a parametrized scalar problem. Under some convexity assumptions, it is shown that dependence of optimal solutions on the parameter is Lipschitz continuous. Hence differentiable dependence on the solutions on the parameter is derived.