Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 217, Issue 2, Pages 394-419Publisher
ELSEVIER
DOI: 10.1016/j.cam.2007.02.012
Keywords
generalized semi-infinite programming; structure of the feasible set; first- and second-order optimality conditions; reduction ansatz; numerical methods; design centering; robust optimization
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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.
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