Applied optimization : formulation and algorithms for engineering systems

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Title:

Personal Author:

Baldick, Ross

Publication Information:

Cambridge, UK : Cambridge University Press, 2006

Physical Description:

xviii, 768 p. : ill. ; 26 cm.

ISBN:

9780521855648

Subject Term:

Systems engineering

Mathematical optimization

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010192447	TA168 B38 2006	Open Access Book	Book	Searching... Unknown

The starting point in the formulation of any numerical problem is to take an intuitive idea about the problem in question and to translate it into precise mathematical language. This book provides step-by-step descriptions of how to formulate numerical problems and develops techniques for solving them. A number of engineering case studies motivate the development of efficient algorithms that involve, in some cases, transformation of the problem from its initial formulation into a more tractable form. Five general problem classes are considered: linear systems of equations, non-linear systems of equations, unconstrained optimization, equality-constrained optimization and inequality-constrained optimization. The book contains many worked examples and homework exercises and is suitable for students of engineering or operations research taking courses in optimization. Supplementary material including solutions, lecture slides and appendices are available online at www.cambridge.org/9780521855648.

Author Notes

Ross Baldick is a professor of electrical and computer engineering at The University of Texas at Austin

Reviews 1

Choice Review

Baldick (electrical engineering, Univ. of Texas at Austin) is known for his research on modeling and optimization of electrical power systems. His book is aimed at graduate students in engineering. The first two sections cover linear and nonlinear systems of equations; this subject is commonly treated in courses in numerical analysis rather than in an optimization course. This material is followed by more conventional sections on unconstrained optimization, equality constrained optimization, and inequality constrained optimization. Two appendixes cover prerequisite mathematics and proofs of the theorems; they are available for download from the publisher's Web site but are not included in the book. Each section of the book begins with several case studies, followed by a discussion of theoretical issues and solution algorithms. Solutions to the case studies are obtained using the MATLAB Optimization Toolbox. Although this would not be an appropriate resource for a more theoretical course in optimization, it may be appropriate for engineering students who want to use optimization software such as the Optimization Toolbox. ^BSumming Up: Optional. Graduate students. B. Borchers New Mexico Institute of Mining and Technology

List of illustrations	p. xii
Preface	p. xvii
1 Introduction	p. 1
1.1 Goals	p. 2
1.2 Course plans	p. 4
1.3 Model formulation and development	p. 4
1.4 Overview	p. 7
1.5 Pre-requisites	p. 14
2 Problems, algorithms, and solutions	p. 15
2.1 Decision vector	p. 16
2.2 Simultaneous equations	p. 16
2.3 Optimization	p. 22
2.4 Algorithms	p. 47
2.5 Solutions of simultaneous equations	p. 54
2.6 Solutions of optimization problems	p. 61
2.7 Sensitivity and large change analysis	p. 80
2.8 Summary	p. 89
3 Transformation of problems	p. 103
3.1 Objective	p. 105
3.2 Variables	p. 122
3.3 Constraints	p. 131
3.4 Duality	p. 139
3.5 Summary	p. 144
Part I Linear simultaneous equations	p. 159
4 Case studies	p. 161
4.1 Analysis of a direct current linear circuit	p. 161
4.2 Control of a discrete-time linear system	p. 176
5 Algorithms	p. 186
5.1 Inversion of coefficient matrix	p. 188
5.2 Solution of triangular systems	p. 189
5.3 Solution of square, non-singular systems	p. 193
5.4 Symmetric coefficient matrix	p. 204
5.5 Sparsity techniques	p. 209
5.6 Changes	p. 219
5.7 Ill-conditioning	p. 227
5.8 Non-square systems	p. 236
5.9 Iterative methods	p. 241
5.10 Summary	p. 242
Part II Non-linear simultaneous equations	p. 257
6 Case studies	p. 259
6.1 Analysis of a non-linear direct current circuit	p. 260
6.2 Analysis of an electric power system	p. 267
7 Algorithms	p. 285
7.1 Newton-Raphson method	p. 286
7.2 Variations on the Newton-Raphson method	p. 291
7.3 Local convergence of iterative methods	p. 298
7.4 Globalization procedures	p. 316
7.5 Sensitivity and large change analysis	p. 324
7.6 Summary	p. 326
8 Solution of the case studies	p. 334
8.1 Analysis of a non-linear direct current circuit	p. 334
8.2 Analysis of an electric power system	p. 340
Part III Unconstrained optimization	p. 361
9 Case studies	p. 363
9.1 Multi-variate linear regression	p. 363
9.2 Power system state estimation	p. 372
10 Algorithms	p. 381
10.1 Optimality conditions	p. 381
10.2 Approaches to finding minimizers	p. 394
10.3 Sensitivity	p. 416
10.4 Summary	p. 419
11 Solution of the case studies	p. 425
11.1 Multi-variate linear regression	p. 425
11.2 Power system state estimation	p. 434
Part IV Equality-constrained optimization	p. 445
12 Case studies	p. 447
12.1 Least-cost production	p. 447
12.2 Power system state estimation with zero injection buses	p. 457
13 Algorithms for linear constraints	p. 463
13.1 Optimality conditions	p. 464
13.2 Convex problems	p. 483
13.3 Approaches to finding minimizers	p. 495
13.4 Sensitivity	p. 509
13.5 Solution of the least-cost production case study	p. 514
13.6 Summary	p. 517
14 Algorithms for non-linear constraints	p. 529
14.1 Geometry and analysis of constraints	p. 530
14.2 Optimality conditions	p. 537
14.3 Approaches to finding minimizers	p. 541
14.4 Sensitivity	p. 545
14.5 Solution of the zero injection bus case study	p. 547
14.6 Summary	p. 549
Part V Inequality-constrained optimization	p. 557
15 Case studies	p. 559
15.1 Least-cost production with capacity constraints	p. 559
15.2 Optimal routing in a data communications network	p. 562
15.3 Least absolute value estimation	p. 572
15.4 Optimal margin pattern classification	p. 576
15.5 Sizing of interconnects in integrated circuits	p. 582
15.6 Optimal power flow	p. 593
16 Algorithms for non-negativity constraints	p. 607
16.1 Optimality conditions	p. 608
16.2 Convex problems	p. 618
16.3 Approaches to finding minimizers: active set method	p. 620
16.4 Approaches to finding minimizers: interior point algorithm	p. 630
16.5 Summary	p. 658
17 Algorithms for linear constraints	p. 669
17.1 Optimality conditions	p. 670
17.2 Convex problems	p. 679
17.3 Approaches to finding minimizers	p. 691
17.4 Sensitivity	p. 697
17.5 Summary	p. 700
18 Solution of the linearly constrained case studies	p. 708
18.1 Least-cost production with capacity constraints	p. 708
18.2 Optimal routing in a data communications network	p. 710
18.3 Least absolute value estimation	p. 712
18.4 Optimal margin pattern classification	p. 712
19 Algorithms for non-linear constraints	p. 723
19.1 Geometry and analysis of constraints	p. 724
19.2 Optimality conditions	p. 727
19.3 Convex problems	p. 731
19.4 Approaches to finding minimizers	p. 738
19.5 Sensitivity	p. 741
19.6 Summary	p. 744
20 Solution of the non-linearly constrained case studies	p. 748
20.1 Optimal margin pattern classification	p. 748
20.2 Sizing of interconnects in integrated circuits	p. 748
20.3 Optimal power flow	p. 750
References	p. 754
Index	p. 762
Appendices (downloadable from www.cambridge.org)
Appendix A Mathematical preliminaries	p. 771
A.1 Notation	p. 771
A.2 Types of functions	p. 777
A.3 Norms	p. 781
A.4 Limits	p. 785
A.5 Sets	p. 789
A.6 Properties of matrices	p. 791
A.7 Special results	p. 795
Appendix B Proofs of theorems	p. 802
B.1 Problems, algorithms, and solutions	p. 802
B.2 Algorithms for linear simultaneous equations	p. 805
B.3 Algorithms for non-linear simultaneous equations	p. 809
B.4 Algorithms for linear equality-constrained minimization	p. 818
B.5 Algorithms for linear inequality-constrained minimization	p. 819
B.6 Algorithms for non-linear inequality-constrained minimization	p. 823

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