最优化导论

内容概要

Rangarajan K.Sundaram，毕业于美国康乃尔大学，哲学博士，工商管理硕士。先后在罗切斯特人学和组约人学斯特恩商学院任教，授课课程涉及微分、期权定价、最优化理论、博弈论、公司理财、经济学原理、中级微观经济学和数理经济学等。研究领域包括：代理问题、管理层薪资水平、公司础财、衍生工具定价、信用风险与信用衍生工具等。他在世界顶级学术期刊上还发表了大量论文。

书籍目录

Mathematical Preliminaries1.1 Notation and Preliminary Definitions1.1.1 Integers, Rationals, Reals, Rn1.1.2 Inner Product, Norm, Metric1.2 Sets and Sequences in Rn1.2.1　Sequences and Limits1.2.2 Subsequences and Limit Points1.2.3 Cauchy Sequences and Completeness1.2.4 Suprema, Infima, Maxima, Minima1.2.5　Monotone Sequences in R1.2.6 The Lim Sup and Lim Inf1.2.7 Open Balls, Open Sets, Closed Sets1.2.8　Bounded Sets and Compact Sets1.2.9 Convex Combinations and Convex Sets1.2.10 Unions, Intersections, and Other Binary Operations1.3 Matrices1.3.1　Sum, Product, Transpose1.3.2 Some Important Classes of Matrices1.3.3 Rank of a Matrix1.3.4　The Determinant1.3.5　The Inverse1.3.6 Calculating the Determinant1.4 Functions1.4.1　Continuous Functions1.4.2 Differentiable and Continuously Differentiable Functions1.4.3 Partial Derivatives and Differentiability1.4.4 Directional Derivatives and Differentiability1.4.5 Higher Order Derivatives1.5 Quadratic Forms: Definite and Semidefinite Matrices1.5.1 Quadratic Forms and Definiteness1.5.2 Identifying Definiteness and Semidefiniteness1.6 Some Important Results1.6.1 Separation Theorems1.6.2 The Intermediate and Mean Value Theorems1.6.3 The Inverse and Implicit Function Theorems1.7 Exercises2 Optimization in R2.1 Optimization Problems in Rn2.2 Optimization Problems in Parametric Form2.3 Optimization Problems: Some Examples2.5 A Roadmap2.6 Exercises3 Existence of Solutions: The Weierstrass Theorem3.1 The Weierstrass Theorem3.2 The Weierstrass Theorem in Applications3.3 A Proof of the Weierstrass Theorem3.4 Exercises4 Unconstrained Optima4.1 "Unconstrained" Optima4.2 First-Order Conditions4.3 Second-Order Conditions4.4 Using the First- and Second-Ordei Conditions4.5 A Proof of the First-Order Conditions4.6 A Proof of the Second-Order Conditions4.7 Exercises5 Equality Constraints and the Theorem of Lagrange5.1 Constrained Optimization Problems5.2 Equality Constraints and the Theorem of Lagrange5.2.1 Statement of the Theorem5.2.2 The Constraint Qualification5.2.3 The Lagrangean Multipliers5.3 Second-Order Conditions5.4 Using the Theorem of Lagrange5.4.1 A "Cookbook" Procedure5.4.2 Why the Procedure Usually Works5.4.3 When It Could Fail5.4.4 A Numerical Example5.5 Two Examples from Economics5.5.1 An Illustration from Consumer Theory5.5.2 An Illustration from Producer Theory5.5.3 Remarks5.6 A Proof of the Theorem of Lagrange5.7 A Proof of the Second-Order Conditions5.8 Exercises6 Inequality Constraints and the Theorem of Kuhn and Tucker6.1 The Theorem of Kuhn and Tucker6.1.1 Statement of the Theorem6.1.2 The Constraint Qualification6.1.3 The Kuhn-Tucker Multipliers6.2 Using the Theorem of Kuhn and Tucker6.2.1 A "Cookbook" Procedure6.2.2 Why the Procedure Usually Works6.2.3 When It Could Fail6.2.4 A Numerical Example6.3 Illustrations from Economics6.3.1 An Illustration from Consumer Theory6.3.2 An Illustration from Producer Theory6.4 The General Case: Mixed Constraints6.5 A Proof of the Theorem of Kuhn and Tucker6.6 Exercises7 Convex Structures in Optimization Theory7.1 Convexity Defined7.1.1 Concave and Convex Functions7.1.2 Strictly Concave and Strictly Convex Functions7.2 Implications of Convexity7.2.1 Convexity and Continuity7.2.2 Convexity and Differentiability7.2.3 Convexity and the Properties of the Derivative7.3 Convexity and Optimization7.3.1 Some General Observations7.3.2 Convexity and Unconstrained Optimization7.3.3 Convexity and the Theorem of Kuhn and Tucker7.4 Using Convexity in Optimization7.5 A Proof of the First-Derivative Characterization of Convexity7.6 A Proof of the Second-Derivative Characterization of Convexity7.7 A Proof of the Theorem of Kuhn and Tucker under Convexity7.8 Exercises8 Quasi-Convexity and Optimization8.1 Quasi-Concave and Quasi-Convex Functions8.2 Quasi-Convexity as a Generalization of Convexity8.3 Implications of Quasi-Convexity8.4 Quasi-Convexity and Optimization8.5 Using Quasi-Convexity in Optimization Problems8.6 A Proof of the First-Derivative Characterization of Quasi-Convexity8.7 A Proof of the Second-Derivative Characterization ofQuasi-Convexity8.8 A Proof of the Theorem of Kuhn and Tucker under Quasi-Convexity8.9 Exercises9 Parametric Continuity: The Maximum Theorem10 Supermodularity and Parametric Monotomicity11 Finite-Horizon Dynamic Programming12 Stationary Discounted Dynamic ProgrammingAppendix A Set Theory and Logic: An IntroductionAppendix B The Real LineBibliographyIndex

编辑推荐

《最优化导论(英文版)》出自纽约大学著名教授之手，被国外众多大学用作教材或主要参考书。如普林斯顿大学、圣路易斯华盛顿大学、宾夕法尼亚大学、马里兰大学等。《最优化导论(英文版)》出版以来。已经重印了10多次，深受广大读者欢迎。最优化是在20世纪得到快速速发展的一门学科。随着计算机技术的发展，它在经济计划、工程设计、生产管理、交通运输、国防等重要领域得到了日益广泛的应用，它已受到政府部门、科研机构和产业部门的高度重视。《最优化导论(英文版)》适合于高等院校经济学、工商管理、保险学、精算学等专业高年级本科生和研究生参考。

作者简介

《最优化导论(英文版)》介绍了最优化理论及其在经济学和相关学科中的应用，全书共分三个部分。第一部分研究了Rn中最优化问题的解的存在性以及如何确定这些解，第二部分探讨了最优化问题的解如何随着基本参数的变化而变化，最后一部分描述了有限维和无限维的动态规划。另外，还给出基础知识准备一章和三个附录，使得《最优化导论(英文版)》自成体系。最优化是在20世纪得到快速发展的一门学科。

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