Introduction to Optimization

Name: Introduction to Optimization
Price: 80.54 USD
Availability: InStock
ISBN: 9780471758006

ISBN-10: 0471758000

ISBN-13: 9780471758006

Edition: 3rd 2008

Authors: Edwin K. P. Chong, Stanislaw H. Zak

List price: $122.00

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Description:

An Introduction to Optimization, Third Edition helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization. The book is supplemented with numerous illustrations, an extensive bibliography, mathematical discussion at a level accessible to MBA and business students, a treatment of both linear and nonlinear programming, an introduction to recent developments such as neural networks and genetic algorithms, a chapter on the use of descent algorithms, and MATLAB exercises and examples.

Book details

List price: $122.00
Edition: 3rd
Copyright year: 2008
Publisher: John Wiley & Sons, Incorporated
Publication date: 2/25/2008
Binding: Hardcover
Pages: 608
Size: 6.50" wide x 9.25" long x 1.25" tall
Weight: 2.134
Language: English



Preface



Mathematical Review



Methods of Proof and Some Notation



Methods of Proof



Notation


Exercises



Vector Spaces and Matrices



Vector and Matrix



Rank of a Matrix



Linear Equations



Inner Products and Norms


Exercises



Transformations



Linear Transformations



Eigenvalues and Eigenvectors



Orthogonal Projections



Quadratic Forms



Matrix Norms


Exercises



Concepts from Geometry



Line Segments



Hyperplanes and Linear Varieties



Convex Sets



Neighborhoods



Polytopes and Polyhedra


Exercises



Elements of Calculus



Sequences and Limits



Differentiability



The Derivative Matrix



Differentiation Rules



Level Sets and Gradients



Taylor Series


Exercises



Unconstrained Optimization



Basics of Set-Constrained and Unconstrained Optimization



Introduction



Conditions for Local Minimizers


Exercises



One-Dimensional Search Methods



Golden Section Search



Fibonacci Search



Newton's Method



Secant Method



Remarks on Line Search Methods


Exercises



Gradient Methods



Introduction



The Method of Steepest Descent



Analysis of Gradient Methods


Exercises



Newton's Method



Introduction



Analysis of Newton's Method



Levenberg-Marquardt Modification



Newton's Method for Nonlinear Least Squares


Exercises



Conjugate Direction Methods



Introduction



The Conjugate Direction Algorithm



The Conjugate Gradient Algorithm



The Conjugate Gradient Algorithm for Nonquadratic


Problems


Exercises



Quasi-Newton Methods



Introduction



Approximating the Inverse Hessian



The Rank One Correction Formula



The DFP Algorithm



The BFGS Algorithm


Exercises



Solving Linear Equations



Least-Squares Analysis



The Recursive Least-Squares Algorithm



Solution to a Linear Equation with Minimum Norm



Kaczmarz's Algorithm



Solving Linear Equations in General


Exercises



Unconstrained Optimization and Neural Networks



Introduction



Single-Neuron Training



The Backpropagation Algorithm


Exercises



Global Search Algorithms



Introduction



The Nelder-Mead Simplex Algorithm



Simulated Annealing



Particle Swarm Optimization



Genetic Algorithms


Exercises



Linear Programming



Introduction to Linear Programming



Brief History of Linear Programming



Simple Examples of Linear Programs



Two-Dimensional Linear Programs



Convex Polyhedra and Linear Programming



Standard Form Linear Programs



Basic Solutions



Properties of Basic Solutions



Geometric View of Linear Programs


Exercises



Simplex Method



Solving Linear Equations Using Row Operations



The Canonical Augmented Matrix



Updating the Augmented Matrix



The Simplex Algorithm



Matrix Form of the Simplex Method



Two-Phase Simplex Method



Revised Simplex Method


Exercises



Duality



Dual Linear Programs



Properties of Dual Problems


Exercises



Nonsimplex Methods



Introduction



Khachiyan's Method



Affine Scaling Method



Karmarkar's Method


Exercises



Nonlinear Constrained Optimization



Problems with Equality Constraints



Introduction



Problem Formulation



Tangent and Normal Spaces



Lagrange Condition



Second-Order Conditions



Minimizing Quadratics Subject to Linear Constraints


Exercises



Problems with Inequality Constraints



Karush-Kuhn-Tucker Condition



Second-Order Conditions


Exercises



Convex Optimization Problems



Introduction



Convex Functions



Convex Optimization Problems



Semidefinite Programming


Exercises



Algorithms for Constrained Optimization



Introduction



Projections



Projected Gradient Methods with Linear Constraints



Lagrangian Algorithms



Penalty Methods


Exercises



Multiobjective Optimization



Introduction



Pareto Solutions



Computing the Pareto Front



From Multiobjective to Single-Objective Optimization



Uncertain Linear Programming Problems


Exercises


References


Index