x CONTENTS
3 Global Convergence 39
3.1 The Method of Steepest Descent ......................... 39
3.2 Line Search Methods and the Armijo Rule .................... 40
3.2.1 Stepsize Control with Polynomial Models ................ 43
3.2.2 Slow Convergence of Steepest Descent ................. 45
3.2.3 Damped Gauss–Newton Iteration .................... 47
3.2.4 Nonlinear Conjugate Gradient Methods ................. 48
3.3 Trust Region Methods ............................... 50
3.3.1 Changing the Trust Region and the Step ................. 51
3.3.2 Global Convergence of Trust Region Algorithms ............ 52
3.3.3 A Unidirectional Trust Region Algorithm ................ 54
3.3.4 The Exact Solution of the Trust Region Problem ............ 55
3.3.5 The Levenberg–Marquardt Parameter .................. 56
3.3.6 Superlinear Convergence: The Dogleg .................. 58
3.3.7 A Trust Region Method for Newton–CG ................. 63
3.4 Examples ..................................... 65
3.4.1 Parameter Identification ......................... 67
3.4.2 Discrete Control Problem ........................ 68
3.5 Exercises on Global Convergence ........................ 68
4 The BFGS Method 71
4.1 Analysis ...................................... 72
4.1.1 Local Theory ............................... 72
4.1.2 Global Theory .............................. 77
4.2 Implementation .................................. 78
4.2.1 Storage .................................. 78
4.2.2 A BFGS–Armijo Algorithm ....................... 80
4.3 Other Quasi-Newton Methods .......................... 81
4.4 Examples ..................................... 83
4.4.1 Parameter ID Problem .......................... 83
4.4.2 Discrete Control Problem ........................ 83
4.5 Exercises on BFGS ................................ 85
5 Simple Bound Constraints 87
5.1 Problem Statement ................................ 87
5.2 Necessary Conditions for Optimality ....................... 87
5.3 Sufficient Conditions ............................... 89
5.4 The Gradient Projection Algorithm ........................ 91
5.4.1 Termination of the Iteration ....................... 91
5.4.2 Convergence Analysis .......................... 93
5.4.3 Identification of the Active Set ...................... 95
5.4.4 A Proof of Theorem 5.2.4 ........................ 96
5.5 Superlinear Convergence ............................. 96
5.5.1 The Scaled Gradient Projection Algorithm ................ 96
5.5.2 The Projected Newton Method ...................... 100
5.5.3 A Projected BFGS–Armijo Algorithm .................. 102
5.6 Other Approaches ................................. 104
5.6.1 Infinite-Dimensional Problems ...................... 106
5.7 Examples ..................................... 106
5.7.1 Parameter ID Problem .......................... 106
5.7.2 Discrete Control Problem ........................ 106
Copyright ©1999 by the Society for Industrial and Applied Mathematics. This electronic version is for personal use and may not be duplicated or distributed.
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mzg123456782020-04-10不错的资源，学习中
iceflyingsouth2012-11-17这本书很好，尤其适合做反问题的同学结合VOGEL的书一起读
