Second-order optimality conditions and Lagrange multiplier characterizations of the solution set in quasiconvex programming
arXiv:1311.2845 · doi:10.1080/02331934.2019.1625351
Abstract
Second-order optimality conditions for vector nonlinear programming problems with inequality constraints are studied in this paper. We introduce a new second-order constraint qualification, which includes Mangasarian-Fromovitz constraint qualification as a particular case. We obtain necessary and sufficient conditions for weak efficiency of problems with a second-order pseudoconvex vector objective function and quasiconvex constraints. We also derive Lagrange multiplier characterizations of the solution set of a scalar problem with a second-order pseudoconvex objective function and quasiconvex inequality constraints, provided that one of the solutions and the Lagrange multipliers in the Karush-Kuhn-Tucker conditions are known. At last, we introduce a notion of a second-order KKT-pseudoconvex problem with inequality constraints. We derive sufficient and also necessary conditions for efficiency of second-order KKT-pseudoconvex problems. Three examples are presented.
The submission contains 15 pages. I replaced the first version of the paper by another one, because I have published the introduced constraint qualification in another article. In this version it is replaced by a new second-order constraint qualification, and therefore a new theorem appears. I have added a new section with new results also