由于此商品库存有限,请在下单后15分钟之内支付完成,手慢无哦!
100%刮中券,最高50元无敌券,券有效期7天
活动自2017年6月2日上线,敬请关注云钻刮券活动规则更新。
如活动受政府机关指令需要停止举办的,或活动遭受严重网络攻击需暂停举办的,或者系统故障导致的其它意外问题,苏宁无需为此承担赔偿或者进行补偿。
醉染图书凸优化算法9787302430704
¥ ×1
Contents
1. Convex Optimization Models: An Overview . . . . . . p. 1
1.1. LagrangeDuality .......... .......... p.2
1.1.1. Separable Problems – Decoition . . . . . . . . . p. 7
1.1.2. Partitioning .................... p.9
1.2. Fenchel Duality and Conic Programming . . . . . . . . . . p. 10
1.2.1. LinearConicProblems . . . . . . . . . . . . . . . p.15
1.2.2. Second Order Cone Programming . . . . . . . . . . . p. 17
1... Semide.nite Programming . . . . . . . . . . . . . . p. 22
1.3. AdditiveCostProblems . . . . . . . . . . . . . . . . . p.25
1.4. LargeNumberofConstraints . . . . . . . . . . . . . . . p.34
1.5. ExactPenalty Functions . . . . . . . . . . . . . . . . p.39
1.6. Notes,Sources,andExercises . . . . . . . . . . . . . . p.47
2. Optimization Algorithms: An Overview . . . . . . . . p. 53
2.1. IterativeDescentAlgorithms . . . . . . . . . . . . . . . p.55
2.1.1. Di.erentiable Cost Function Descent – Unconstrained . . . . Problems ..................... p.58
2.1.2. Constrained Problems – Feasible Direction Methods . . . p. 71
2.1.3. Nondi.erentiable Problems – Subgradient Methods . . . p. 78
2.1.4. Alternative Descent Methods . . . . . . . . . . . . . p. 80
2.1.5. IncrementalAlgorithms . . . . . . . . . . . . . . . p.83
2.1.6. Distributed Asynchronous Iterative Algorithms . . . . p. 104
2.2. ApproximationMethods . . . . . . . . . . . . . . . p.106
2.2.1. Poleral Approximation . . . . . . . . . . . . . p. 107
2.2.2. Penalty, Augmented Lagrangian, and Interior . . . . . . . PointMethods .................. p.108
2... Proximal Algorithm, Bundle Methods, and . . . . . . . . . TikhonovRegularization . . . . . . . . . . . . . . p.110
2.2.4. Alternating Direction Method of Multipliers . . . . . p. 111
2.2.5. Smoothing of Nondi.erentiable Problems . . . . . . p. 113
.. Notes,Sources,andExercises . . . . . . . . . . . . . p.119
3. SubgradientMethods . . . . . . . . . . . . . . . p.135
3.1. Subgradients of Convex Real-Valued Functions . . . . . . p. 136
iv
Contents
3.1.1. Characterization of the Subdi.erential . . . . . . . . p. 146
3.2. Convergence Analysis of Subgradient Methods . . . . . . p. 148
3.3. .-SubgradientMethods ................ p.162
3.3.1. Connection with Incremental Subgradient Methods . . p. 166
3.4. Notes,Sources,andExercises . . . . . . . . . . . . . . p.167
4. Poleral Approximation Methods . . . . . . . . . p. 181
4.1. Outer Linearization – Cutting Plane Methods . . . . . . p. 182
4.2. Inner Linearization – Simpli Decoition . . . . . . p. 188
4.3. Duality of Outer and Inner Linearization . . . . . . . . . p. 194
4.4. Generalized Poleral Approximation . . . . . . . . . p. 196
4.5. Generalized Simpli Decoition . . . . . . . . . . p. 209
4.5.1. Di.erentiableCostCase . . . . . . . . . . . . . . p.213
4.5.2. Nondi.erentiable Cost and Side Constraints . . . . . p. 213
4.6. Poleral Approximation for Conic Programming . . . . p. 217
4.7. Notes,Sources,andExercises . . . . . . . . . . . . . . p.228
5. ProximalAlgorithms . . . . . . . . . . . . . . . p.
5.1. Basic Theory of Proximal Algorithms . . . . . . . . . . p. 4
5.1.1. Convergence ................... p.5
5.1.2. RateofConvergence. . . . . . . . . . . . . . . . p.
5.1.3. Gradient Interpretation . . . . . . . . . . . . . . p. 246
5.1.4. Fixed Point Interpretation, Overrelaxation, . . . . . . . . . andGeneralization ................ p.248
5.2. DualProximalAlgorithms . . . . . . . . . . . . . . . p.256
5.2.1. Augmented Lagrangian Methods . . . . . . . . . . p. 259
5.3. Proximal Algorithms with Linearization . . . . . . . . . p. 268
5.3.1. Proximal Cutting Plane Methods . . . . . . . . . . p. 270
5.3.2. BundleMethods ................. p.272
5.3.3. Proximal Inner Linearization Methods . . . . . . . . p. 276
5.4. Alternating Direction Methods of Multipliers . . . . . . . p. 280
5.4.1. Applications in Machine Learning . . . . . . . . . . p. 286
5.4.2. ADMM Applied to Separable Problems . . . . . . . p. 289
5.5. Notes,Sources,andExercises . . . . . . . . . . . . . . p.293
6. Additional Algorithmic Topics . . . . . . . . . . . p. 301
6.1. GradientProjectionMethods . . . . . . . . . . . . . . p.302
6.2. Gradient Projection with Extrapolation . . . . . . . . . p. 322
6.2.1. An Algorithm with Optimal Iteration Comlxiy&bsp;. . . p. 3
6.2.2. Nondi.erentiable Cost – Smoothing . . . . . . . . . p. 326
6.3. ProximalGradientMethods . . . . . . . . . . . . . . p.330
6.4. Incremental Subgradient Proximal Methods . . . . . . . p. 340
6.4.1. Convergence for Methods with Cyclic Order . . . . . p. 344
Contents
6.4.2. Convergence for Methods with Randomized Order . . p. 353
6.4.3. Application in Spely Structured Problems . . . . . p. 361
6.4.4. Incremental Constraint Projection Methods . . . . . p. 365
6.5. CoordinateDescentMethods . . . . . . . . . . . . . . p.369
6.5.1. Variants of Coordinate Descent . . . . . . . . . . . p. 373
6.5.2. Distributed Asynchronous Coordinate Descent . . . . p. 376
6.6. Generalized Proximal Methods . . . . . . . . . . . . . p. 382
6.7. .-Descent and Extended Monotropic Programming . . . . p. 396
6.7.1. .-Subgradients .................. p.397
6.7.2. .-DescentMethod........ ......... p.400
6.7.3. Extended Monotropic Programming Duality . . . . . p. 406
6.7.4. Spe Cases of Strong Duality . . . . . . . . . . . p. 408
6.8. InteriorPointMethods . . . . . . . . . . . . . . . . p.412
6.8.1. Primal-Dual Methods for Linear Programming . . . . p. 416
6.8.2. Interior Point Methods for Conic Programming . . . . p. 4
6.8.3. Central Cutting Plane Methods . . . . . . . . . . . p. 425
6.9. Notes,Sources,andExercises . . . . . . . . . . . . . . p.426
Appendix A: Mathematical Background . . . . . . . . p. 443
A.1. LinearAlgebra ........... ......... p.445
A.2. TopologicalProperties . . . . . . . . . . . . . . . . p.450
A.3. Derivatives ..................... p.456
A.4. ConvergenceTheorems . . . . . . . . . . . . . . . . p.458
Appendix B: Convex Optimization Theory: A Summary . p. 467
B.1. Basic Concepts of Convex Analysis . . . . . . . . . . . p. 467
B.2. Basic Concepts of Poleral Convexity . . . . . . . . . p. 489
B.3. Basic Concepts of Convex Optimization . . . . . . . . . p. 494
B.4. Geometric Duality Framework . . . . . . . . . . . . . p. 498
B.5. Duality andOptimization . . . . . . . . . . . . . . . p.505
References .............. ......... p.519
Index ................. ......... p.557
博塞斯(Dimitri P.Bertsekas)教授是优化理论的靠前有名学者、美国工程院院士,现任美国麻省理工学院电气工程与计算机科学系教授,曾在斯坦福大学工程经济系和伊利诺伊大学电气工程系任教,在优化理论、控制工程、通信工程、计算机科学等领域有丰富的科研教学经验,成果丰硕。博塞斯教授是一位多产作者,著有14本专著和教科书。
随着大规模资源分配、信号处理、机器学习等应用领域的快展,凸优化近来正引起人们日益浓厚的兴趣。本书力图给大家较为全面通俗地介绍求解大规模凸优化问题的近期新算法。本书几乎囊括了所有主流的凸优化算法。包括梯度法,次梯度法,多面体逼近法,邻近法和内点法等。这些方法通常依赖于代价函数和约束条件的凸(而不一定依赖于其可微),并与对偶有着直接或间接的联系。作者针对具体问题的特定结构,给出了大量的例题,来充分展示算法的应用。
亲,大宗购物请点击企业用户渠道>小苏的服务会更贴心!
亲,很抱歉,您购买的宝贝销售异常火爆让小苏措手不及,请稍后再试~
非常抱歉,您前期未参加预订活动,
无法支付尾款哦!
抱歉,您暂无任性付资格