最優(yōu)化導論

內容概要

　　最優(yōu)化是在20世紀得到快速發(fā)展的一門學科。本書介紹了最優(yōu)化理論及其在經濟學和相關學科中的應用，全書共分三個部分。第一部分研究了Rn中最優(yōu)化問題的解的存在性以及如何確定這些解，第二部分探討了最優(yōu)化問題的解如何隨著基本參數(shù)的變化而變化，最后一部分描述了有限維和無限維的動態(tài)規(guī)劃。另外，還給出基礎知識準備一章和三個附錄，使得本書自成體系?！　”緯m合于高等院校經濟學、工商管理、保險學、精算學等專業(yè)高年級本科生和研究生參考。

作者簡介

Rangarajan K.Sundaram，畢業(yè)于美國康乃爾大學，哲學博士，工商管理碩士。先后在羅切斯特人學和組約人學斯特恩商學院任教，授課課程涉及微分、期權定價、最優(yōu)化理論、博弈論、公司理財、經濟學原理、中級微觀經濟學和數(shù)理經濟學等。研究領域包括：代理問題、管理層薪資水平、公司礎財、衍生工具定價、信用風險與信用衍生工具等。他在世界頂級學術期刊上還發(fā)表了大量論文。

書籍目錄

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

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《最優(yōu)化導論(英文版)》出自紐約大學著名教授之手，被國外眾多大學用作教材或主要參考書。如普林斯頓大學、圣路易斯華盛頓大學、賓夕法尼亞大學、馬里蘭大學等?！蹲顑?yōu)化導論(英文版)》出版以來。已經重印了10多次，深受廣大讀者歡迎。最優(yōu)化是在20世紀得到快速速發(fā)展的一門學科。隨著計算機技術的發(fā)展，它在經濟計劃、工程設計、生產管理、交通運輸、國防等重要領域得到了日益廣泛的應用，它已受到政府部門、科研機構和產業(yè)部門的高度重視。《最優(yōu)化導論(英文版)》適合于高等院校經濟學、工商管理、保險學、精算學等專業(yè)高年級本科生和研究生參考。

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