Abstract
This tutorial presents an introduction to generalized semi-infinite programming (GSIP) which in recent years became a vivid field of active research in mathematical programming. A GSIP problem is characterized by an infinite number of inequality constraints, and the corresponding index set depends additionally on the decision variables. There exist a wide range of applications which give rise to GSIP models; some of them are discussed in the present paper. Furthermore, geometric and topological properties of the feasible set and, in particular, the difference to the standard semi-infinite case are analyzed. By using first-order approximations of the feasible set corresponding constraint qualifications are developed. Then, necessary and sufficient first- and second-order optimality conditions are presented where directional differentiability properties of the optimal value function of the so-called lower level problem are used. Finally, an overview of numerical methods is given. (C) 2007 Elsevier B.V. All rights reserved.
| Original language | English |
|---|---|
| Pages (from-to) | 394-419 |
| Number of pages | 26 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 217 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Aug 2008 |
Keywords
- design centering
- structure of the feasible set
- reduction ansatz
- first- and second-order optimality conditions
- generalized semi-infinite programming
- robust optimization
- numerical methods