无约束最优化与非线性方程的数值方法
2009-1
科学出版社
（美）丹尼斯（Dennis，J.E.） 等著
378
要使我国的数学事业更好地发展起来，需要数学家淡泊名利并付出更艰苦地努力。另一方面，我们也要从客观上为数学家创造更有利的发展数学事业的外部环境，这主要是加强对数学事业的支持与投资力度，使数学家有较好的工作与生活条件，其中也包括改善与加强数学的出版工作。从出版方面来讲，除了较好较快地出版我们自己的成果外，引进国外的先进出版物无疑也是十分重要与必不可少的。从数学来说，施普林格（springer）出版社至今仍然是世界上最具权威的出版社。科学出版社影印一批他们出版的好的新书，使我国广大数学家能以较低的价格购买，特别是在边远地区工作的数学家能普遍见到这些书，无疑是对推动我国数学的科研与教学十分有益的事。这次科学出版社购买了版权，一次影印了23本施普林格出版社出版的数学书，就是一件好事，也是值得继续做下去的事情。大体上分一下，这23本书中，包括基础数学书5本，应用数学书6本与计算数学书12本，其中有些书也具有交叉性质。这些书都是很新的，2000年以后出版的占绝大部分，共计16本，其余的也是1990年以后出版的。这些书可以使读者较快地了解数学某方面的前沿，例如基础数学中的数论、代数与拓扑三本，都是由该领域大数学家编著的“数学百科全书”的分册。对从事这方面研究的数学家了解该领域的前沿与全貌很有帮助。按照学科的特点，基础数学类的书以“经典”为主，应用和计算数学类的书以“前沿”为主。这些书的作者多数是国际知名的大数学家，例如《拓扑学》一书的作者诺维科夫是俄罗斯科学院的院士，曾获“菲尔兹奖”和“沃尔夫数学奖”。这些大数学家的著作无疑将会对我国的科研人员起到非常好的指导作用。当然，23本书只能涵盖数学的一部分，所以，这项工作还应该继续做下去。更进一步，有些读者面较广的好书还应该翻译成中文出版，使之有更大的读者群。总之，我对科学出版社影印施普林格出版社的部分数学著作这一举措表示热烈的支持，并盼望这一工作取得更大的成绩。
This book is a standard for a complete description of the methods for unconstrained optimization and the solution ofnonlinear equations....this republication is most welcome and this volume should be in every library. Of course, there exist more recent books on the topics and somebody interested in the subject cannot be satiated by looking only at this book. However, it contains much quite-well-presented material and I recommend reading it before going ,to other.publications.
作者：(美国)丹尼斯 (J.E.Dennis Jr.) (美国)Robert B.Schnabel
PREFACE TO THE CLASSICS EDITION PREFACE 1 INTRODUCTION 1.1 Problems to be considered 1.2 Characteristics of"real-world" problems 1.3 Finite-precision arithmetic and measurement of error 1.4 Exercises 2 NONLINEAR PROBLEMS IN ONE VARIABLE 2.1 What is not possible 2.2 Newton's method for solving one equation in one unknown 2.3 Convergence of sequences of real numbers 2.4 Convergence of Newton's method 2.5 Globally convergent methods for solving one equation in one unknown 2.6 Methods when derivatives are unavailable 2.7 Minimization of a function of one variable 2.8 Exercises 3 NUMERICAL LINEAR ALGEBRA BACKGROUND 3.1 Vector and matrix norms and orthogonality 3.2 Solving systems of linear equations--matrix factorizations 3.3 Errors in solving linear systems 3.4 Updating matrix factorizations 3.5 Eigenvalues and positive definiteness 3.6 Linear least squares 3.7 Exercises 4 MULTIVARIABLE CALCULUS BACKGROUND 4.1 Derivatives and multivariable models 4.2 Multivariable finite-difference derivatives 4.3 Necessary and sufficient conditions for unconstrained minimization 4.4 Exercises 835 NEWTON'S METHOD FOR NONLINEAR EQUATIONS AND UNCONSTRAINED MINIMIZATION 5.1 Newton's method for systems of nonlinear equations 5.2 Local convergence of Newton's method 5.3 The Kantorovich and contractive mapping theorems 5.4 Finite-difference derivative methods for systems of nonlinear equations 5.5 Newton's method for unconstrained minimization 5.6 Finite-difference derivative methods for unconstrained minimization 5.7 Exercises 6 GLOBALLY CONVERGENT MODIFICATIONS OF NEWTON'S METHOD 6.1 The quasi-Newton framework 6.2 Descent directions 6.3 Line searches 6.3.1 Convergence results for properly chosen steps 6.3.2 Step selection by backtracking 6.4 The model-trust region approach 6.4.1 The locally constrained optimal ("hook") step 6.4.2 The double dogleg step 6.4.3 Updating the trust region 6.5 Global methods for systems of nonlinear equations 6.6 Exercises 7 STOPPING, SCALING, AND TESTING 7.1 Scaling 7.2 Stopping criteria 7.3 Testing 7.4 Exercises 8 SECANT METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS 8.1 Broyden's method 8.2 Local convergence analysis of Broyden's method 8.3 Implementation of quasi-Newton algorithms using Broyden's update 8.4 Other secant updates for nonlinear equations 8.5 Exercises 9 SECANT METHODS FOR UNCONSTRAINED MINIMIZATION 9.1 The symmetric secant update of Powell 9.2 Symmetric positive definite secant updates 9.3 Local convergence of positive definite secant methods 9.4 Implementation of quasi-Newton algorithms using the positive definite secant update 9.5 Another convergence result for the positive definite secant method 9.6 Other secant updates for unconstrained minimization 9.7 Exercises 10 NONLINEAR LEAST SQUARES 10.1 The nonlinear least-squares problem 10.2 Gauss-Newton-type methods 10.3 Full Newton-type methods 10.4 Other considerations in solving nonlinear least-squares problems 10.5 Exercises 11 METHODS FOR PROBLEMS WITH SPECIAL STRUCTURE 11.1 The sparse finite-difference Newton method 11.2 Sparse secant methods 11.3 Deriving least-change secant updates 11.4 Analyzing least-change secant methods 11.5 Exercises A APPENDIX: A MODULAR SYSTEM OF ALGORITHMS FOR UNCONSTRAINED MINIMIZATION AND NONLINEAR EQUATIONS (by Robert Schnabel)B APPENDIX: TEST PROBLEMS (by Robert SchnabeI) REFERENCES AUTHOR INDEX SUBJECT INDEX
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《国外数学名著系列(续1)(影印版)42:无约束最优化与非线性方程的数值方法》由科学出版社出版。
是优化和数值代数最经典的教材之一，做数值代数的学者要读的课本。
翻印的，很好的书，便宜，原版的买不起
这本书买来两个月了，还没看完，不过其中的算法思想很值得一看。
刚拿到书，大牛写的书应该没得挑
无约束最优化与非线性方程组的数值解法这本书很不错