Practical optimization : algorithms and engineering applications

Select an Action

Place Hold(s)
Add to My Lists
Email
Print

Title:

Personal Author:

Antoniou, Andreas

Publication Information:

New York, NY : Springer, 2007

ISBN:

9780387711065

Subject Term:

Mathematical optimization

Added Author:

Murray, Walter

Wright, Margaret H.

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010160374	QA402.5 A574 2007	Open Access Book	Book	Searching... Unknown

Practical Optimization: Algorithms and Engineering Applications is a hands-on treatment of the subject of optimization. A comprehensive set of problems and exercises makes the book suitable for use in one or two semesters of a first-year graduate course or an advanced undergraduate course. Each half of the book contains a full semester's worth of complementary yet stand-alone material. The practical orientation of the topics chosen and a wealth of useful examples also make the book suitable for practitioners in the field.

Author Notes

Andreas Antoniou received the Ph.D. degree in Electrical Engineering from the University of London, UK, in 1966 and is a Fellow of the IET and IEEE. He served as the founding Chair of the Department of Electrical and Computer Engineering at the University of Victoria, B.C., Canada, and is now Professor Emeritus in the same department. He is the author of Digital Filters: Analysis, Design, and Applications (McGraw-Hill, 1993) and Digital Signal Processing: Signals, Systems, and Filters (McGraw-Hill, 2005). He served as Associate Editor/Editor of IEEE Transactions on Circuits and Systems from June 1983 to May 1987, as a Distinguished Lecturer of the IEEE Signal Processing Society in 2003, as General Chair of the 2004 International Symposium on Circuits and Systems, and is currently serving as a Distinguished Lecturer of the IEEE Circuits and Systems Society. He received the Ambrose Fleming Premium for 1964 from the IEEE (best paper award), the CAS Golden Jubilee Medal from the IEEE Circuits and Systems Society, the B.C. Science Council Chairman's Award for Career Achievement for 2000, theDoctorHonoris Causa degree from the Metsovio National Technical University of Athens, Greece, in 2002, and the IEEE Circuits and Systems Society 2005 Technical Achievement Award.

Wu-Sheng Lu received the B.S. degree in Mathematics from Fudan University, Shanghai, China, in 1964, the M.E. degree in Automation from the East China Normal University, Shanghai, in 1981, the M.S. degree in Electrical Engineering and the Ph.D. degree in Control Science from the University of Minnesota, Minneapolis, in 1983 and 1984, respectively. He was a post-doctoral fellow at the University of Victoria, Victoria, BC, Canada, in 1985 and Visiting Assistant Professor with the University of Minnesota in 1986. Since 1987, he has been with the University of Victoria where he is Professor. His current teaching and research interests are in the general areas of digital signal processing and application of optimization methods. He is the co-author with A. Antoniou of Two-Dimensional Digital Filters (Marcel Dekker, 1992). He served as an Associate Editor of the Canadian Journal of Electrical and Computer Engineering in 1989, and Editor of the same journal from 1990 to 1992. He served as an Associate Editor for the IEEE Transactions on Circuits and Systems, Part II, from 1993 to 1995 and for Part I of the same journal from 1999 to 2001 and from 2004 to 2005. Presently he is serving as Associate Editor for the International Journal of Multidimensional Systems and Signal Processing. He is a Fellow of the Engineering Institute of Canada and the Institute of Electrical and Electronics Engineers.

Dedication	p. v
Biographies of the authors	p. vii
Preface	p. xv
Abbreviations	p. xix
1 The Optimization Problem	p. 1
1.1 Introduction	p. 1
1.2 The Basic Optimization Problem	p. 4
1.3 General Structure of Optimization Algorithms	p. 8
1.4 Constraints	p. 10
1.5 The Feasible Region	p. 17
1.6 Branches of Mathematical Programming	p. 22
References	p. 24
Problems	p. 25
2 Basic Principles	p. 27
2.1 Introduction	p. 27
2.2 Gradient Information	p. 27
2.3 The Taylor Series	p. 28
2.4 Types of Extrema	p. 31
2.5 Necessary and Sufficient Conditions for Local Minima and Maxima	p. 33
2.6 Classification of Stationary Points	p. 40
2.7 Convex and Concave Functions	p. 51
2.8 Optimization of Convex Functions	p. 58
References	p. 60
Problems	p. 60
3 General Properties of Algorithms	p. 65
3.1 Introduction	p. 65
3.2 An Algorithm as a Point-to-Point Mapping	p. 65
3.3 An Algorithm as a Point-to-Set Mapping	p. 67
3.4 Closed Algorithms	p. 68
3.5 Descent Functions	p. 71
3.6 Global Convergence	p. 72
3.7 Rates of Convergence	p. 76
References	p. 79
Problems	p. 79
4 One-Dimensional Optimization	p. 81
4.1 Introduction	p. 81
4.2 Dichotomous Search	p. 82
4.3 Fibonacci Search	p. 85
4.4 Golden-Section Search	p. 92
4.5 Quadratic Interpolation Method	p. 95
4.6 Cubic Interpolation	p. 99
4.7 The Algorithm of Davies, Swann, and Campey	p. 101
4.8 Inexact Line Searches	p. 106
References	p. 114
Problems	p. 114
5 Basic Multidimensional Gradient Methods	p. 119
5.1 Introduction	p. 119
5.2 Steepest-Descent Method	p. 120
5.3 Newton Method	p. 128
5.4 Gauss-Newton Method	p. 138
References	p. 140
Problems	p. 140
6 Conjugate-Direction Methods	p. 145
6.1 Introduction	p. 145
6.2 Conjugate Directions	p. 146
6.3 Basic Conjugate-Directions Method	p. 149
6.4 Conjugate-Gradient Method	p. 152
6.5 Minimization of Nonquadratic Functions	p. 157
6.6 Fletcher-Reeves Method	p. 158
6.7 Powell's Method	p. 159
6.8 Partan Method	p. 168
References	p. 172
Problems	p. 172
7 Quasi-Newton Methods	p. 175
7.1 Introduction	p. 175
7.2 The Basic Quasi-Newton Approach	p. 176
7.3 Generation of Matrix S[subscript k]	p. 177
7.4 Rank-One Method	p. 181
7.5 Davidon-Fletcher-Powell Method	p. 185
7.6 Broyden-Fletcher-Goldfarb-Shanno Method	p. 191
7.7 Hoshino Method	p. 192
7.8 The Broyden Family	p. 192
7.9 The Huang Family	p. 194
7.10 Practical Quasi-Newton Algorithm	p. 195
References	p. 199
Problems	p. 200
8 Minimax Methods	p. 203
8.1 Introduction	p. 203
8.2 Problem Formulation	p. 203
8.3 Minimax Algorithms	p. 205
8.4 Improved Minimax Algorithms	p. 211
References	p. 228
Problems	p. 228
9 Applications of Unconstrained Optimization	p. 231
9.1 Introduction	p. 231
9.2 Point-Pattern Matching	p. 232
9.3 Inverse Kinematics for Robotic Manipulators	p. 237
9.4 Design of Digital Filters	p. 247
References	p. 260
Problems	p. 262
10 Fundamentals of Constrained Optimization	p. 265
10.1 Introduction	p. 265
10.2 Constraints	p. 266
10.3 Classification of Constrained Optimization Problems	p. 273
10.4 Simple Transformation Methods	p. 277
10.5 Lagrange Multipliers	p. 285
10.6 First-Order Necessary Conditions	p. 294
10.7 Second-Order Conditions	p. 302
10.8 Convexity	p. 308
10.9 Duality	p. 311
References	p. 312
Problems	p. 313
11 Linear Programming Part I: The Simplex Method	p. 321
11.1 Introduction	p. 321
11.2 General Properties	p. 322
11.3 Simplex Method	p. 344
References	p. 368
Problems	p. 368
12 Linear Programming Part II: Interior-Point Methods	p. 373
12.1 Introduction	p. 373
12.2 Primal-Dual Solutions and Central Path	p. 374
12.3 Primal Affine-Scaling Method	p. 379
12.4 Primal Newton Barrier Method	p. 383
12.5 Primal-Dual Interior-Point Methods	p. 388
References	p. 402
Problems	p. 402
13 Quadratic and Convex Programming	p. 407
13.1 Introduction	p. 407
13.2 Convex QP Problems with Equality Constraints	p. 408
13.3 Active-Set Methods for Strictly Convex QP Problems	p. 411
13.4 Interior-Point Methods for Convex QP Problems	p. 417
13.5 Cutting-Plane Methods for CP Problems	p. 428
13.6 Ellipsoid Methods	p. 437
References	p. 443
Problems	p. 444
14 Semidefinite and Second-Order Cone Programming	p. 449
14.1 Introduction	p. 449
14.2 Primal and Dual SDP Problems	p. 450
14.3 Basic Properties of SDP Problems	p. 455
14.4 Primal-Dual Path-Following Method	p. 458
14.5 Predictor-Corrector Method	p. 465
14.6 Projective Method of Nemirovski and Cabinet	p. 470
14.7 Second-Order Cone Programming	p. 484
14.8 A Primal-Dual Method for SOCP Problems	p. 491
References	p. 496
Problems	p. 497
15 General Nonlinear Optimization Problems	p. 501
15.1 Introduction	p. 501
15.2 Sequential Quadratic Programming Methods	p. 501
15.3 Modified SQP Algorithms	p. 509
15.4 Interior-Point Methods	p. 518
References	p. 528
Problems	p. 529
16 Applications of Constrained Optimization	p. 533
16.1 Introduction	p. 533
16.2 Design of Digital Filters	p. 534
16.3 Model Predictive Control of Dynamic Systems	p. 547
16.4 Optimal Force Distribution for Robotic Systems with Closed Kinematic Loops	p. 558
16.5 Multiuser Detection in Wireless Communication Channels	p. 570
References	p. 586
Problems	p. 588
Appendices	p. 591
A Basics of Linear Algebra	p. 591
A.1 Introduction	p. 591
A.2 Linear Independence and Basis of a Span	p. 592
A.3 Range, Null Space, and Rank	p. 593
A.4 Sherman-Morrison Formula	p. 595
A.5 Eigenvalues and Eigenvectors	p. 596
A.6 Symmetric Matrices	p. 598
A.7 Trace	p. 602
A.8 Vector Norms and Matrix Norms	p. 602
A.9 Singular-Value Decomposition	p. 606
A.10 Orthogonal Projections	p. 609
A.11 Householder Transformations and Givens Rotations	p. 610
A.12 QR Decomposition	p. 616
A.13 Cholesky Decomposition	p. 619
A.14 Kronecker Product	p. 621
A.15 Vector Spaces of Symmetric Matrices	p. 623
A.16 Polygon, Polyhedron, Polytope, and Convex Hull	p. 626
References	p. 627
B Basics of Digital Filters	p. 629
B.1 Introduction	p. 629
B.2 Characterization	p. 629
B.3 Time-Domain Response	p. 631
B.4 Stability Property	p. 632
B.5 Transfer Function	p. 633
B.6 Time-Domain Response Using the Z Transform	p. 635
B.7 Z-Domain Condition for Stability	p. 635
B.8 Frequency, Amplitude, and Phase Responses	p. 636
B.9 Design	p. 639
Reference	p. 644
Index	p. 645

Available:*

On Order

Summary

Summary

Author Notes

Table of Contents