- Title
- Second-order variational analysis in conic programming with applications to optimality and stability
- Creator
- Mordukhovich, Boris; Outrata, Jiri; Ramírez, Hector
- Date
- 2015
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/77111
- Identifier
- vital:7676
- Identifier
-
https://doi.org/10.1137/120903221
- Identifier
- ISSN:1052-6234
- Abstract
- This paper is devoted to the study of a broad class of problems in conic programming modeled via parameter-dependent generalized equations. In this framework we develop a second-order generalized differential approach of variational analysis to calculate appropriate derivatives and coderivatives of the corresponding solution maps. These developments allow us to resolve some important issues related to conic programming. They include verifiable conditions for isolated calmness of the considered solution maps, sharp necessary optimality conditions for a class of mathematical programs with equilibrium constraints, and characterizations of tilt-stable local minimizers for cone-constrained problems. The main results obtained in the general conic programming setting are specified for and illustrated by the second-order cone programming. © 2015 Society for Industrial and Applied Mathematics.
- Relation
- SIAM Journal on Optimization Vol. 25, no. 1 (2015), p. 76-101; http://purl.org/au-research/grants/arc/DP110102011
- Rights
- Copyright Society for Industrial and Applied Mathematics Publications
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- Conic programming; Generalized differentiation; Isolated calmness; Optimality conditions; Second-order theory; Tilt stability; Variational analysis; 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics
- Full Text
- Reviewed
- Hits: 2550
- Visitors: 2960
- Downloads: 377
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE1 | Published version | 360 KB | Adobe Acrobat PDF | View Details Download |