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线性和非线性规划 第3版 英文PDF|Epub|txt|kindle电子书版本网盘下载
- （美）吕恩博格著 著
- 出版社： 北京：世界图书北京出版公司
- ISBN：9787510094736
- 出版时间：2015
- 标注页数：549页
- 文件大小：74MB
- 文件页数：564页
- 主题词：非线性规划－英文；线性规划－英文
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图书目录
Chapter 1．Introduction1
1.1．Optimization1
1.2．Types of Problems2
1.3．Size of Problems5
1.4．Iterative Algorithms and Convergence6
PART Ⅰ Linear Programming11
Chapter 2．Basic Properties of Linear Programs11
2.1．Introduction11
2.2．Examples of Linear Programming Problems14
2.3．Basic Solutions19
2.4．The Fundamental Theorem of Linear Programming20
2.5．Relations to Convexity22
2.6．Exercises28
Chapter 3．The Simplex Method33
3.1．Pivots33
3.2．Adjacent Extreme Points38
3.3．Determining a Minimum Feasible Solution42
3.4．Computational Procedure—Simplex Method46
3.5．Artificial Variables50
3.6．Matrix Form of the Simplex Method54
3.7．The Revised Simplex Method56
3.8．The Simplex Method and LU Decomposition59
3.9．Decomposition62
3.10．Summary70
3.11．Exercises70
Chapter 4．Duality79
4.1．Dual Linear Programs79
4.2．The Duality Theorem82
4.3．Relations to the Simplex Procedure84
4.4．Sensitivity and Complementary Slackness88
4.5．The Dual Simplex Method90
4.6．The Primal-Dual Algorithm93
4.7．Reduction of Linear Inequalities98
4.8．Exercises103
Chapter 5．Interior-Point Methods111
5.1．Elements of Complexity Theory112
5.2．The Simplex Method is not Polynomial-Time114
5.3．The Ellipsoid Method115
5.4．The Analytic Center118
5.5．The Central Path121
5.6．Solution Strategies126
5.7．Termination and Initialization134
5.8．Summary139
5.9．Exercises140
Chapter 6．Transportation and Network Flow Problems145
6.1．The Transportation Problem145
6.2．Finding a Basic Feasible Solution148
6.3．Basis Triangularity150
6.4．Simplex Method for Transportation Problems153
6.5．The Assignment Problem159
6.6．Basic Network Concepts160
6.7．Minimum Cost Flow162
6.8．Maximal Flow166
6.9．Summary174
6.10．Exercises175
PART Ⅱ Unconstrained Problems183
Chapter 7．Basic Properties of Solutions and Algorithms183
7.1．First-Order Necessary Conditions184
7.2．Examples of Unconstrained Problems186
7.3．Second-Order Conditions190
7.4．Convex and Concave Functions192
7.5．Minimization and Maximization of Convex Functions197
7.6．Zero-Order Conditions198
7.7．Global Convergence of Descent Algorithms201
7.8．Speed of Convergence208
7.9．Summary212
7.10．Exercises213
Chapter 8．Basic Descent Methods215
8.1．Fibonacci and Golden Section Search216
8.2．Line Search by Curve Fitting219
8.3．Global Convergence of Curve Fitting226
8.4．Closedness of Line Search Algorithms228
8.5．Inaccurate Line Search230
8.6．The Method of Steepest Descent233
8.7．Applications of the Theory242
8.8．Newton's Method246
8.9．Coordinate Descent Methods253
8.10．Spacer Steps255
8.11．Summary256
8.12．Exercises257
Chapter 9．Conjugate Direction Methods263
9.1．Conjugate Directions263
9.2．Descent Properties of the Conjugate Direction Method266
9.3．The Conjugate Gradient Method268
9.4．The C-G Method as an Optimal Process271
9.5．The Partial Conjugate Gradient Method273
9.6．Extension to Nonquadratic Problems277
9.7．Parallel Tangents279
9.8．Exercises282
Chapter 10．Quasi-Newton Methods285
10.1．Modified Newton Method285
10.2．Construction of the Inverse288
10.3．Davidon-Fletcher-Powell Method290
10.4．The Broyden Family293
10.5．Convergence Properties296
10.6．Scaling299
10.7．Memoryless Quasi-Newton Methods304
10.8．Combination of Steepest Descent and Newton's Method306
10.9．Summary312
10.10．Exercises313
PART Ⅲ Constrained Minimization321
Chapter 11．Constrained Minimization Conditions321
11.1．Constraints321
11.2．Tangent Plane323
11.3．First-Order Necessary Conditions(Equality Constraints)326
11.4．Examples327
11.5．Second-Order Conditions333
11.6．Eigenvalues in Tangent Subspace335
11.7．Sensitivity339
11.8．Inequality Constraints341
11.9．Zero-Order Conditions and Lagrange Multipliers346
11.10．Summary353
11.11．Exercises354
Chapter 12．Primal Methods359
12.1．Advantage of Primal Methods359
12.2．Feasible Direction Methods360
12.3．Active Set Methods363
12.4．The Gradient Projection Method367
12.5．Convergence Rate of the Gradient Projection Method374
12.6．The Reduced Gradient Method382
12.7．Convergence Rate of the Reduced Gradient Method387
12.8．Variations394
12.9．Summary396
12.10．Exercises396
Chapter 13．Penalty and Barrier Methods401
13.1．Penalty Methods402
13.2．Barrier Methods405
13.3．Properties of Penalty and Barrier Functions407
13.4．Newton's Method and Penalty Functions416
13.5．Conjugate Gradients and Penalty Methods418
13.6．Normalization of Penalty Functions420
13.7．Penalty Functions and Gradient Projection421
13.8．Exact Penalty Functions425
13.9．Summary429
13.10．Exercises430
Chapter 14．Dual and Cutting Plane Methods435
14.1．Global Duality435
14.2．Local Duality441
14.3．Dual Canonical Convergence Rate446
14.4．Separable Problems447
14.5．Augmented Lagrangians451
14.6．The Dual Viewpoint456
14.7．Cutting Plane Methods460
14.8．Kelley's Convex Cutting Plane Algorithm463
14.9．Modifications465
14.10．Exercises466
Chapter 15．Primal-Dual Methods469
15.1．The Standard Problem469
15.2．Strategies471
15.3．A Simple Merit Function472
15.4．Basic Primal-Dual Methods474
15.5．Modified Newton Methods479
15.6．Descent Properties481
15.7．Rate of Convergence485
15.8．Interior Point Methods487
15.9．Semidefinite Programming491
15.10．Summary498
15.11．Exercises499
Appendix A．Mathemtical Review507
A.1．Sets507
A.2．Matrix Notation508
A.3．Spaces509
A.4．Eigenvalues and Quadratic Forms510
A.5．Topological Concepts511
A.6．Functions512
Appendix B．Convex Sets515
B.1．Basic Definitions515
B.2．Hyperplanes and Polytopes517
B.3．Separating and Supporting Hyperplanes519
B.4．Extreme Points521
Appendix C．Gaussian Elimination523
Bibliography527
Index541