An Introduction to Optimization, Second Edition
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More About This Title An Introduction to Optimization, Second Edition
English
EDWIN K. P. CHONG, PhD, is Professor of Electrical and Computer Engineering at Colorado State University, Fort Collins, Colorado. He was an Associate Editor for the IEEE Transactions on Automatic Control and received the 1998 ASEE Frederick Emmons Terman Award.
STANISLAW H. ZAK, PhD, is Professor in the School of Electrical and Computer Engineering at Purdue University, West Lafayette, Indiana. He was an Associate Editor of Dynamics and Control and the IEEE Transactions on Neural Networks.
STANISLAW H. ZAK, PhD, is Professor in the School of Electrical and Computer Engineering at Purdue University, West Lafayette, Indiana. He was an Associate Editor of Dynamics and Control and the IEEE Transactions on Neural Networks.
English
Preface. xiii
PART I MATHEMATICAL REVIEW
Methods of Proof and Some Notation 1
Vector Spaces and Matrices 5
Transformations 21
Concepts from Geometry 39
Elements of Calculus 49
Part II UNCONSTRAINED OPTIMIZATION
Basics of Set-Constrained and Unconstrained Optimization 73
One-Dimensional Search Methods 91
Gradient Methods 113
Newton's Method 139
Conjugate Direction Methods 151
Quasi-Newton Methods 167
Solving Ax = b 187
Unconstrained Optimization and Neural Networks 219
Genetic Algorithms 237
Part III LINEAR PROGRAMMING
Introduction to Linear Programming. 255
Simplex Method 287
Duality 321
Non-Simplex Methods 339
Part IV NONLINEAR CONSTRAINED OPTIMIZATION
Problems with Equality Constraints 365
Problems with Inequality Constraints 397
Convex Optimization Problems 417
Algorithms for Constrained Optimization 439
References 455
Index 462
PART I MATHEMATICAL REVIEW
Methods of Proof and Some Notation 1
Vector Spaces and Matrices 5
Transformations 21
Concepts from Geometry 39
Elements of Calculus 49
Part II UNCONSTRAINED OPTIMIZATION
Basics of Set-Constrained and Unconstrained Optimization 73
One-Dimensional Search Methods 91
Gradient Methods 113
Newton's Method 139
Conjugate Direction Methods 151
Quasi-Newton Methods 167
Solving Ax = b 187
Unconstrained Optimization and Neural Networks 219
Genetic Algorithms 237
Part III LINEAR PROGRAMMING
Introduction to Linear Programming. 255
Simplex Method 287
Duality 321
Non-Simplex Methods 339
Part IV NONLINEAR CONSTRAINED OPTIMIZATION
Problems with Equality Constraints 365
Problems with Inequality Constraints 397
Convex Optimization Problems 417
Algorithms for Constrained Optimization 439
References 455
Index 462
English
"...an excellent introduction to optimization theory..." (Journal of Mathematical Psychology, 2002)
"A textbook for a one-semester course on optimization theory and methods at the senior undergraduate or beginning graduate level." (SciTech Book News, Vol. 26, No. 2, June 2002)
