Second-order optimality conditions and Lagrange multiplier characterizations of the solution set in quasiconvex programming. (2nd April 2020)

• Record Type: Journal Article
• Authors: Ivanov, Vsevolod I.
• Is Part Of: Optimization. Volume 69:Number 4(2020)
• Page Start: 637
• Page End: 655
• Publication Date: 2020-04-02
• Subjects: Multiobjective nonsmooth optimization -- Karush-Kuhn-Tucker optimality conditions -- characterizations of the solution set -- second-order pseudoconvex function -- second-order Mangasarian-Fromovitz constraint qualifications; 90C46 -- 90C26 -- 90C29 -- 26B25 -- 49J52; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1625351
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: Second-order optimality conditions for the vector nonlinear programming problems with inequality constraints and continuously differentiable data 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 notions of a second-order pseudoconvex vector function and KKT-pseudoconvex vector problem with inequality constraints. We derive necessary and sufficient conditions for efficiency in the vector problem with inequality constraints. Three examples are presented.