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Book Categories |
List of Symbols | ||
List of Figures | ||
List of Tables | ||
Preface | ||
Acknowledgments | ||
1 | Introduction | 1 |
1.1 | Standard semi-infinite programming | 2 |
1.2 | General semi-infinite programming | 4 |
1.3 | The misconception about the generality of GSIP | 6 |
1.4 | Development to a field of active research | 8 |
2 | Examples and Applications | 11 |
2.1 | Chebyshev and reverse Chebyshev approximation | 12 |
2.2 | Minimax problems | 14 |
2.3 | Robust optimization | 15 |
2.4 | Design centering | 18 |
2.5 | Defect minimization for operator equations | 20 |
2.6 | Disjunctive programming | 22 |
3 | Topological Structure of the Feasible Set | 25 |
3.1 | Abstract index set mappings | 25 |
3.2 | Index set mappings with functional constraints | 46 |
4 | Optimality Conditions | 85 |
4.1 | Abstract primal optimality conditions | 85 |
4.2 | First order approximations of the feasible set | 90 |
4.3 | Dual first order optimality conditions | 116 |
4.4 | Second order optimality conditions | 142 |
5 | Bi-Level Methods for GSIP | 145 |
5.1 | Reformulations of GSIP | 146 |
5.2 | Convergence results for a bi-level method | 154 |
5.3 | Other bi-level approaches and generalizations | 167 |
6 | Computational Results | 171 |
6.1 | Design centering in two dimensions | 172 |
6.2 | Design centering in higher dimensions | 177 |
6.3 | Robust optimization | 178 |
6.4 | Optimal error bounds for an elliptic operator equation | 181 |
7 | Final Remarks | 187 |
References | 191 | |
Index | 201 |
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