Bounded sets of Lagrange multipliers for vector optimization problems in infinite dimension
The paper starts with a short history of the method of Lagrange multipliers in constrained optimization problem. Contributions of Kuhn-Tucker, John, Mangasarian-Fromowitz conducted Gavin to prove that some constraint qualifications are in fact equivalent, in some conditions, to the boundedness of the set of Lagrange multipliers. The authors extend this result to the cone constrained vector optimization problem in infinite dimension. They study the smooth and nonsmooth case. The authors take a unified view by studying set-valued optimization problem in terms of the coderivative of Mordukhovitch.
scientific article; zbMATH DE number 5355959
scientific article