| List of Figures | 10 |
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| Contents | 7 |
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| Preface | 11 |
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| Preliminaries | 18 |
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| 1.1 Some preliminaries from convex analysis | 18 |
| 1.2 Some preliminaries from abstract convex analysis | 44 |
| 1.3 Duality for best approximation by elements of convex sets | 56 |
| 1.4 Duality for convex and quasi-convex infimization | 63 |
| Worst Approximation | 102 |
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| 2.1 The deviation of a set from an element | 103 |
| 2.2 Characterizations and existence of farthest points | 110 |
| Duality for Quasi- convex Supremization | 118 |
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| 3.1 Some hyperplane theorems of surrogate duality | 120 |
| 3.2 Unconstrained surrogate dual problems for quasi- convex supremization | 125 |
| 3.3 Constrained surrogate dual problems for quasi- convex supremization | 138 |
| 3.4 Lagrangian duality for convex supremization | 144 |
| 3.5 Duality for quasi-convex supremization over structured primal constraint sets | 148 |
| Optimal Solutions for Quasi- convex Maximization | 153 |
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| 4.1 Maximum points of quasi- convex functions | 153 |
| 4.2 Maximum points of continuous convex functions | 160 |
| 4.3 Some basic subdifferential characterizations of maximum points | 165 |
| Reverse Convex Best Approximation | 169 |
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| 5.1 The distance to the complement of a convex set | 170 |
| 5.2 Characterizations and existence of elements of best approximation in complements of convex sets | 177 |
| Unperturbational Duality for Reverse Convex Infimization | 184 |
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| 6.1 Some hyperplane theorems of surrogate duaUty | 186 |
| 6.2 Unconstrained surrogate dual problems for reverse convex infimization | 190 |
| 6.3 Constrained surrogate dual problems for reverse convex infimization | 199 |
| 6.4 Unperturbational Lagrangian duality for reverse convex infimization | 204 |
| 6.5 Duality for infimization over structured primal reverse convex constraint sets | 205 |
| Optimal Solutions for Reverse Convex Infimization | 217 |
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| 7.1 Minimum points of functions on reverse convex subsets of locally convex spaces | 217 |
| 7.2 Subdifferential characterizations of minimum points of functions on reverse convex sets | 223 |
| Duality for D.C. Optimization Problems | 227 |
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| 8.1 Unperturbational duality for unconstrained d. c. infimization | 227 |
| 8.2 Minimum points of d. c. functions | 235 |
| 8.3 Duality for d. c. infimization with a d. c. inequality constraint | 239 |
| 8.4 Duality for d. c. infimization with finitely many d. c. inequality constraints | 246 |
| 8.5 Perturbational theory | 258 |
| 8.6 Duality for optimization problems involving maximum operators | 261 |
| Duality for Optimization in the Framework of Abstract Convexity | 273 |
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| 9.1 Additional preliminaries from abstract convex analysis | 273 |
| 9.2 Surrogate duality for abstract quasi- convex supremization, using polarities Ac: 2X -- | 273 |
| 9.2 Surrogate duality for abstract quasi- convex supremization, using polarities Ac: 2X -- | 273 |
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| 281 | 273 |
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| 9.3 Constrained surrogate duality for abstract quasi-convex supremization, using families of subsets of X | 284 |
| 9.4 Surrogate duality for abstract reverse convex infimization, using polarities AG : 2X - | 284 |
| 9.4 Surrogate duality for abstract reverse convex infimization, using polarities AG : 2X - | 284 |
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| 285 | 284 |
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| 9.5 Constrained surrogate duality for abstract reverse convex infimization, using families of subsets of X | 287 |
| 9.6 Duality for unconstrained abstract d. c. infimization | 289 |
| Notes and Remarks | 292 |
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| References | 341 |
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| Index | 358 |