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Full Description
This book provides an introduction to optimization theory and its applications. It is written for senior undergraduate students and first-year graduate students of telecommunication and related fields. Most applications pertain to communication and network problems. The book has practical examples to accompany rigorous discussion so that the reader may develop intuitive understanding on relevant concepts. The materials have been developed from course notes. By attempting to cover convex, linear, and integer optimization for a one-semester course, the author focuses on fundamental concepts and techniques rather than trying to be comprehensive. Infact, the book is written with the main intention to serve as a bridge for students with no prior background in optimization to be able to access more advanced books on the subject later on.
Contents
Preface List of Figures Introduction Components of Optimization Problems Classes of Optimization Problems Convex Optimization Convex Sets and Convex Functions Properties of Convex Optimization Further Properties of Convex Sets Dual Problems Lagrange Multipliers Primal-Dual Optimality Conditions Sensitivity Analysis Notes on Maximization Problems Numerical Algorithms for Unconstrained Optimization Numerical Algorithms for Constrained Optimization Application: Transmit Power Allocation Application: Minimum Delay Routing Exercise Problems Linear Optimization Illustrative Example Properties of Linear Optimization Problems Simplex Algorithm Duality for Linear Optimization Application: Minimum Cost Routing 983.6 Application: Maximum Lifetime Routing in a WSN Exercise Problems Integer Linear Optimization Illustrative Examples Branch-and-Bound Cutting-Plane Algorithm Duality for Integer Linear Optimization Heuristics for Integer Linear Optimization Application: RWA in a WDM Network Application: Network Topology Design Exercise Problems Appendix A: Reviews of Related Mathematics Review of Linear Algebra Review of Analysis Appendix B: Solutions to Exercise Problems Appendix C: Octave Commands for Optimization Minimum Cost Routing Maximum Lifetime Routing in a WSN RWA in a WDM Network Network Topology Design Bibliography Index
