On second-order optimality conditions for vector optimization
A vector optimization problem (VOP) is considered. The feasible set is stated by means of equality and inequality constraints. Two constraint qualifications has been borrowed from the scalar case and used for VOP. The first one (Kuhn-Tucker constraint qualification KTCQ) is based on a feasible arc and implies that the set of feasible and descent directions is empty if the considered point verifies the KTCQ. The second -- the constant rank constraint qualification (CRCQ) -- was introduced by Janin. A second-order necessary condition is established assuming an adopted second-order constraint qualification, originally proposed for the scalar case. By strengthening this first-order constraint qualification, a similar result is obtained, with effective intervention of all the objective functions. The CRCQ is proved to be a second-order qualification for the VOP so that a second-order necessary condition is obtained for VOP with general nonlinear constraints, without any convexity assumptions.
scientific article; zbMATH DE number 5942039
scientific article