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Second-order optimality conditions and Lagrange multiplier characterizations of the solution set in quasiconvex programming
| Content Provider | Scilit |
|---|---|
| Author | Ivanov, Vsevolod I. |
| Copyright Year | 2019 |
| Description | 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. |
| Related Links | http://arxiv.org/pdf/1311.2845 |
| Ending Page | 655 |
| Page Count | 19 |
| Starting Page | 637 |
| ISSN | 02331934 |
| e-ISSN | 10294945 |
| DOI | 10.1080/02331934.2019.1625351 |
| Journal | Optimization |
| Issue Number | 4 |
| Volume Number | 69 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2020-04-02 |
| Access Restriction | Open |
| Subject Keyword | Journal: Optimization Applied Mathematics 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 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Control and Optimization Applied Mathematics Management Science and Operations Research |
