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図書

東工大
目次DB

図書
東工大
目次DB
by Hiroshi Konno, Phan Thien Thach, Hoang Tuy
出版情報: Dordrecht : Kluwer Academic, c1997  xi, 457 p. ; 25 cm
シリーズ名: Nonconvex optimization and its applications ; v. 15
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PREFACE
Part I FOUNDATIONS 1
   1 SCOPE OF GLOBAL OPTIMIZATION 3
   1.1 Models and Nature of the Problem 4
   1.2 Mathematical Structure 10
   1.3 Hierarchy of Global Optimization Problems 13
   1.4 Transcending Stationarity as the Core of Global Optimization 15
   1.5 Problems With Special Structures 18
   2 QUASI-CONVEXITY 23
   2.1 Quasi-Convex Functions 24
   2.2 Quasi-conjugacy 30
   2.3 Quasi-biconjugate 39
   2.4 Quasi-subdifferential 43
   3 D.C. FUNCTIONS AND D.C. SETS 47
   3.1 Some Typical Examples 47
   3.2 General Properties of D.C. Functions 50
   3.3 How to Recognize D.C. Functions 52
   3.4 Effective D.C. Representation 56
   3.5 D.C. Sets 67
   3.6 Global Optimality Criterion 72
   4 DUALITY 77
   4.1 Quasi-convex Minimization over a Convex Set 78
   4.2 Maximization over a Convex Set and Minimization over the Complement of a Convex Set 85
   4.3 D.C. Optimization 93
   5 LOW-RANK NONCONVEX STRUCTURES 95
   5.1 Nonconvexity Rank 96
   5.2 Nonconvexity Index 100
   5.3 Weakly Convex Functions 108
   5.4 D.C. Representation by a Nucleus 113
   6 GLOBAL SEARCH METHODS AND BASIC D.C. OPTIMIZATION ALGORITHMS 119
   6.1 Outer Approximation 119
   6.2 Successive Partition 130
   6.3 Dualization 155
Part II METHODS AND ALGORITHMS 167
   7 PARAMETRIC APPROACHES IN GLOBAL OPTIMIZATION 169
   7.1 Minimization of a Generalized Linear Multiplicative Function and a Sum of Two Linear Fractional Functions 170
   7.2 Rank Two and Rank Three Bilinear Programming Problems 177
   7.3 Average Performance of Parametric Algorithms 184
   7.4 Minimization of Low-Rank Concave Functions 191
   8 MULTIPLICATIVE PROGRAMMING PROBLEMS 203
   8.1 Convex Multiplicative Programming Problems 204
   8.2 Minimization of a Product of Several Convex Functions 213
   8.3 Other Problems Related to Multiplicative Functions 220
   9 MONOTONIC PROBLEMS 229
   9.1 Quasiconcave Monotonic Functions 230
   9.2 Basic Structural Properties 234
   9.3 Linearly Constrained Problems 240
   9.4 Solution Methods for Monotonic Problems 244
   9.5 Decomposition by Polyhedral Annexation 247
   9.6 Decomposition by Projection 252
   9.7 Problems With Monotonic Constraints 258
   9.8 Cases of Polynomial Solvability: Network Constraints 264
   10 DECOMPOSITION METHODS BY PRICES 273
   10.1 Generalized Dantzig-Wolfe's Decomposition Method 274
   10.2 Generalized Benders' Partitioning Method 283
   10.3 Alternative Variant 291
   11 DYNAMIC PROGRAMMING ALGORITHMS IN GLOBAL OPTIMIZATION 297
   11.1 Multi-Echelon Production and Inventory Problem 298
   11.2 Lot-Sizing Problems with Generalized Concave Cost Functions 303
   11.3 Discrete-Variable Multi-Stage Problems 310
Part III SELECTED APPLICATIONS 323
   12 LOW RANK NONCONVEX QUADRATIC PROGRAMMING 325
   12.1 Concave Quadratic Programming Problems and Bilinear Programming Problems 326
   12.2 Low Rank Concave Quadratic Programming Problems 331
   12.3 Low Rank Bilinear Programming Problems 343
   12.4 General Low Rank Nonconvex Quadratic Programming Problems 349
   13 CONTINUOUS LOCATION 353
   13.1 Unconstrained Location Problems 354
   13.2 Solving Unconstrained Location Problems 362
   13.3 Constrained Location Problems 367
   13.4 Solving General Constrained Location Problems 371
   14 DESIGN CENTERING AND RELATED GEOMETRIC PROBLEMS 375
   14.1 Design Centering 375
   14.2 Related Geometric Problems 389
   15 MULTIOBJECTIVE AND BILEVEL PROGRAMMING 397
   15.1 Optimization over the Efficient Set 398
   15.2 Bilevel Linear Programming 408
   15.3 Relationship between Monotonic, Multiobjective and Bilevel Programming 423
REFERENCES 427
INDEX 455
PREFACE
Part I FOUNDATIONS 1
   1 SCOPE OF GLOBAL OPTIMIZATION 3
2.

図書

図書
by Hoang Tuy
出版情報: Dordrecht : Kluwer Academic Publishers, c1998  xi, 339 p. ; 25 cm
シリーズ名: Nonconvex optimization and its applications ; v. 22
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