Optimization: A Theory of Necessary Conditions, Neustadt Lucien W.

Автор: Sundaram, Rangarajan K.
Название: A First Course in Optimization Theory
ISBN: 0521497701 ISBN-13(EAN): 9780521497701
Издательство: Cambridge Academ
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Цена: 45410.00 T
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Описание: This book, first published in 1996, introduces students to optimization theory and its use in economics and allied disciplines.

Автор: Wenyu Sun; Ya-Xiang Yuan
Название: Optimization Theory and Methods
ISBN: 144193765X ISBN-13(EAN): 9781441937650
Издательство: Springer
Цена: 121110.00 T
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Описание: Preface 1 Introduction 1.1 Introduction 1.2 Mathematics Foundations 1.2.1 Norm 1.2.2 Inverse and Generalized Inverse of a Matrix 1.2.3 Properties of Eigenvalues 1.2.4 Rank-One Update 1.2.5 Function and Differential 1.3 Convex Sets and Convex Functions 1.3.1 Convex Sets 1.3.2 Convex Functions 1.3.3 Separation and Support of Convex Sets 1.4 Optimality Conditions for Unconstrained Case 1.5 Structure of Optimization Methods Exercises 2 Line Search 2.1 Introduction 2.2 Convergence Theory for Exact Line Search 2.3 Section Methods 2.3.1 The Golden Section Method 2.3.2 The Fibonacci Method 2.4 Interpolation Method 2.4.1 Quadratic Interpolation Methods 2.4.2 Cubic Interpolation Method 2.5 Inexact Line Search Techniques 2.5.1 Armijo and Goldstein Rule 2.5.2 Wolfe-Powell Rule 2.5.3 Goldstein Algorithm and Wolfe-Powell Algorithm 2.5.4 Backtracking Line Search 2.5.5 Convergence Theorems of Inexact Line Search Exercises 3 Newton's Methods 3.1 The Steepest Descent Method 3.1.1 The Steepest Descent Method 3.1.2 Convergence of the Steepest Descent Method 3.1.3 Barzilai and Borwein Gradient Method 3.1.4 Appendix: Kantorovich Inequality 3.2 Newton's Method 3.3 Modified Newton's Method 3.4 Finite-Difference Newton's Method 3.5 Negative Curvature Direction Method 3.5.1 Gill-Murray Stable Newton's Method 3.5.2 Fiacco-McCormick Method 3.5.3 Fletcher-Freeman Method 3.5.4 Second-Order Step Rules 3.6 Inexact Newton's Method Exercises 4 Conjugate Gradient Method 4.1 Conjugate Direction Methods 4.2 Conjugate Gradient Method 4.2.1 Conjugate Gradient Method 4.2.2 Beale's Three-Term Conjugate Gradient Method 4.2.3 Preconditioned Conjugate Gradient Method 4.3 Convergence of Conjugate Gradient Methods 4.3.1 Global Convergence of Conjugate Gradient Methods 4.3.2 Convergence Rate of Conjugate Gradient Methods Exercises 5 Quasi-Newton Methods 5.1 Quasi-Newton Methods 5.1.1 Quasi-Newton Equation 5.1.2 Symmetric Rank-One (SR1) Update 5.1.3 DFP Update 5.1.4 BFGS Update and PSB Update 5.1.5 The Least Change Secant Update 5.2 The Broyden Class 5.3 Global Convergence of Quasi-Newton Methods 5.3.1 Global Convergence under Exact Line Search 5.3.2 Global Convergence under Inexact Line Search 5.4 Local Convergence of Quasi-Newton Methods 5.4.1 Superlinear Convergence of General Quasi-Newton Methods 5.4.2 Linear Convergence of General Quasi-Newton Methods 5.4.3 Local Convergence of Broyden's Rank-One Update 5.4.4 Local and Linear Convergence of DFP Method 5.4.5 Superlinear Convergence of BFGS Method 5.4.6 Superlinear Convergence of DFP Method 5.4.7 Local Convergence of Broyden's Class Methods 5.5 Self-Scaling Variable Metric (SSVM) Methods 5.5.1 Motivation to SSVM Method 5.5.2 Self-Scaling Variable Metric (SSVM) Method 5.5.3 Choices of the Scaling Factor 5.6 Sparse Quasi-Newton Methods 5.7 Limited Memory BFGS Method Exercises 6 Trust-Region and Conic Model Methods 6.1 Trust-Region Methods 6.1.1 Trust-Region Methods 6.1.2 Convergence of Trust-Region Methods 6.1.3 Solving A Trust-Region Subproblem 6.2 Conic Model and Collinear Scaling Algorithm 6.2.1 Conic Model 6.2.2 Generalized Quasi-Newton Equation 6.2.3 Updates that Preserve Past Information 6.2.4 Collinear Scaling BFGS Algorithm 6.3 Tensor Methods 6.3.1 Tensor Method for Nonlinear Equations 6.3.2 Tensor Methods for Unconstrained Optimization Exercises

Автор: Saoussen Krichen,Jouhaina Chaouachi
Название: Graph?€“related Optimization and Decision Theory
ISBN: 1848217439 ISBN-13(EAN): 9781848217430
Издательство: Wiley
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Цена: 146730.00 T
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Constrained optimization is a challenging branch of operationsresearch that aims to create a model which has a wide range ofapplications in the supply chain, telecommunications and medicalfields. As the problem structure is split into two main components, the objective is to accomplish the feasible set framed by thesystem constraints. The aim of this book is expose optimizationproblems that can be expressed as graphs, by detailing, for eachstudied problem, the set of nodes and the set of edges. Thisgraph modeling is an incentive for designing a platform thatintegrates all optimization components in order to output the bestsolution regarding the parameters' tuning. The authors propose intheir analysis, for optimization problems, to provide theirgraphical modeling and mathematical formulation and expose some oftheir variants. As a solution approaches, an optimizer can be themost promising direction for limited-size instances. For largeproblem instances, approximate algorithms are the most appropriateway for generating high quality solutions. The authors thuspropose, for each studied problem, a greedy algorithm as aproblem-specific heuristic and a genetic algorithm as ametaheuristic.