数值最优化（第二版）
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作者（美）乔治 劳斯特等
出版社科学出版社
ISBN9787030605511
出版时间2023-12
装帧精装
开本16开
定价198元
货号26918000
上书时间2024-10-26
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导语摘要
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目录
Preface
prefcetothe Second Edition
1 Introduction
Mathematical Formulation
Example:A Transportation Problem
Continuous versus Discrete Optimization
Constrained and Unconstrained Optimization
Global and Local Optimization
Stocbastic and Deterministic Optimization
Convexity
Optimization Algorithms
Notes and References
2 Fundamentals of Unconstrained Optimization
2.1 What ls a Solution?
Recognizing a Local Minimum
Nonsmooth Problems
2.2 Overview of A1gorithms
Two Strategies:Line Search and Trust Region
Search Directions for Line Search Methods
Models for Trust-Region Methods
Scaling
Exercises
3 Line Search Methods
3.1 Step Length
The Wolfe Conditions
The Goldstein Conditions
Sufficient Decrease and Backtracking
3.2 Convergence of Line Search Methods
3.3 Rate of Convergence
Convergence Rate of Steepest Descent
Newton's Method
Quasi-Newton Methods
3.4 Newton's Method with Hessian Modification
Eigenvalue Modification
Adding a Multiple of the ldentity
Modified Cholesky Factorization
Modified Symmetric Indefinite Factorization
3.5 Step-Length Selection Algorithms
lnterpolation
lnitial Step Length
A Line Search A1gorithm for the Wolfe Conditions
Notes and References
Exercises
4 Trust-Region Methods
Outline of the Trust-Region Approach
4.1 A1gorithms Based on the Cauchy Point
The Cauchy Point
lmpro时ng on the Cauchy Point
The Dogleg Method
Two-Dinlensional Subspace Mininlization
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