Engineering Optimization : Theory and Practice

Engineering Optimization : Theory and Practice
复制标题

DOI：
10.1002/9780470549124
复制
发表时间：
2010-08
期刊：
--
影响因子：
--
通讯作者：
Singiresu S. Rao
Singiresu S. Rao
中科院分区：
其他
文献类型：
--
作者：
Singiresu S. Rao

文献摘要

被引文献

相似文献

前言 1. 优化导论 1.1 引言 1.2 历史发展 1.3 优化的工程应用 1.4 优化问题的陈述 1.5 优化问题的分类 1.6 优化技术 1.7 工程优化文献 1.8 使用MATLAB解决优化问题 参考文献与参考书目 复习题 习题 2. 经典优化技术 2.1 引言 2.2 单变量优化 2.3 无约束多变量优化 2.4 等式约束多变量优化 2.5 不等式约束多变量优化 2.6 凸规划问题 参考文献与参考书目 复习题 习题 3. 线性规划I：单纯形法 3.1 引言 3.2 线性规划的应用 3.3 线性规划问题的标准形式 3.4 线性规划问题的几何 3.5 定义与定理 3.6 线性联立方程组的求解 3.7 一般方程组的枢轴约简 3.8 单纯形法的动机 3.9 单纯形算法 3.10 单纯形法的两个阶段 3.11 线性规划问题的MATLAB解法 参考文献与参考书目 复习题 习题 4. 线性规划II：其他主题与扩展 4.1 引言 4.2 修正单纯形法 4.3 线性规划中的对偶性 4.4 分解原理 4.5 灵敏度或后优化分析 4.6 运输问题 4.7 卡马卡尔的内点法 4.8 二次规划 4.9 MATLAB解法 参考文献与参考书目 复习题 习题 5. 非线性规划I：一维极小化方法 5.1 引言 5.2 单峰函数。消除方法 5.3 无限制搜索 5.4 穷举搜索 5.5 二分搜索 5.6 区间平分法 5.7 斐波那契方法 5.8 黄金分割法 5.9 消除方法的比较。插值方法 5.10 二次插值法 5.11 三次插值法 5.12 直接求根方法 5.13 实际考虑因素 5.14 一维极小化问题的MATLAB解法 参考文献与参考书目 复习题 习题 6. 非线性规划II：无约束优化技术 6.1 引言。直接搜索方法 6.2 随机搜索方法 6.3 网格搜索方法 6.4 单变量方法 6.5 模式方向 6.6 鲍威尔方法 6.7 单纯形方法。间接搜索（下降）方法 6.8 函数的梯度 6.9 最速下降（柯西）方法 6.10 共轭梯度（弗莱彻 - 里夫斯）方法 6.11 牛顿方法 6.12 马夸特方法 6.13 拟牛顿方法 6.14 戴维登 - 弗莱彻 - 鲍威尔方法 6.15 布罗伊登 - 弗莱彻 - 戈德法布 - 香农方法 6.16 测试函数 6.17 无约束优化问题的MATLAB解法 参考文献与参考书目 复习题 习题 7. 非线性规划III：约束优化技术 7.1 引言 7.2 约束问题的特征。直接方法 7.3 随机搜索方法 7.4 复合方法 7.5 序列线性规划 7.6 可行方向法的基本方法 7.7 祖滕迪克的可行方向法 7.8 罗森的梯度投影法 7.9 广义简约梯度法 7.10 序列二次规划。间接方法 7.11 变换技术 7.12 罚函数法的基本方法 7.13 内点罚函数法 7.14 凸规划问题 7.15 外点罚函数法 7.16 内点罚函数法中的外推技术 7.17 扩展内点罚函数法 7.18 混合等式与不等式约束问题的罚函数法 7.19 含参数约束问题的罚函数法 7.20 增广拉格朗日乘子法 7.21 约束优化问题收敛性的检验 7.22 测试问题 7.23 约束优化问题的MATLAB解法 参考文献与参考书目 复习题 习题 8. 几何规划 8.1 引言 8.2 正项式 8.3 无约束极小化问题 8.4 用微分学解决无约束几何规划问题 8.5 用算术 - 几何不等式解决无约束几何规划问题 8.6 无约束情况下的原始 - 对偶关系及充分性条件 8.7 约束极小化 8.8 约束几何规划问题的解决 8.9 小于不等式情况下的原始和对偶规划 8.10 混合不等式约束的几何规划 8.11 互补几何规划 8.12 几何规划的应用 参考文献与参考书目 复习题 习题 9. 动态规划 9.1 引言 9.2 多阶段决策过程 9.3 次优化概念及最优性原理 9.4 动态规划的计算过程 9.5 用微积分解法示例 9.6 用表格解法示例 9.7 将终值问题转化为初值问题 9.8 线性规划作为动态规划的一个案例 9.9 连续动态规划 9.10 其他应用 参考文献与参考书目 复习题 习题 10. 整数规划 10.1 引言588. 整数线性规划 10.2 图形表示 10.3 戈莫里的割平面法 10.4 巴拉什的0 - 1规划问题算法。整数非线性规划 10.5 整数多项式规划 10.6 分支定界法 10.7 序列线性离散规划 10.8 广义罚函数法 10.9 用MATLAB解决二进制规划问题 参考文献与参考书目 复习题 习题 11. 随机规划 11.1 引言 11.2 概率论的基本概念 11.3 随机线性规划 11.4 随机非线性规划 11.5 随机几何规划 参考文献与参考书目 复习题 习题 12. 最优控制与最优性准则方法 12.1 引言 12.2 变分法 12.3 最优控制理论 12.4 最优性准则方法 参考文献与参考书目 复习题 习题 13. 现代优化方法 13.1 引言 13.2 遗传算法 13.3 模拟退火 13.4 粒子群优化 13.5 蚁群优化 13.6 模糊系统优化 13.7 基于神经网络的优化 参考文献与参考书目 复习题 习题 14. 优化的实际方面 14.1 引言 14.2 优化问题规模的缩减 14.3 快速再分析技术 14.4 静态位移和应力的导数 14.5 特征值和特征向量的导数 14.6 瞬态响应的导数 14.7 最优解对问题参数的敏感性 14.8 多层优化 14.9 并行处理 14.10 多目标优化 14.11 用MATLAB解决多目标问题 参考文献与参考书目 复习题 习题 A. 凸函数和凹函数 B. 优化的一些计算方面 B.1 方法的选择 B.2 无约束方法的比较 B.3 约束方法的比较 B.4 计算机程序的可用性 B.5 设计变量和约束的缩放 B.6 现代优化方法的计算机程序 参考文献与参考书目 C. MATLAB(R) 简介 C.1 特征与特殊字符 C.2 在MATLAB中定义矩阵 C.3 创建m - 文件 C.4 优化工具箱 部分习题答案 索引
Preface. 1 Introduction to Optimization. 1.1 Introduction. 1.2 Historical Development. 1.3 Engineering Applications of Optimization. 1.4 Statement of an Optimization Problem. 1.5 Classification of Optimization Problems. 1.6 Optimization Techniques. 1.7 Engineering Optimization Literature. 1.8 Solution of Optimization Problems Using MATLAB. References and Bibliography. Review Questions. Problems. 2 Classical Optimization Techniques. 2.1 Introduction. 2.2 Single-Variable Optimization. 2.3 Multivariable Optimization with No Constraints. 2.4 Multivariable Optimization with Equality Constraints. 2.5 Multivariable Optimization with Inequality Constraints. 2.6 Convex Programming Problem. References and Bibliography. Review Questions. Problems. 3 Linear Programming I: Simplex Method. 3.1 Introduction. 3.2 Applications of Linear Programming. 3.3 Standard Form of a Linear Programming Problem. 3.4 Geometry of Linear Programming Problems. 3.5 Definitions and Theorems. 3.6 Solution of a System of Linear Simultaneous Equations. 3.7 Pivotal Reduction of a General System of Equations. 3.8 Motivation of the Simplex Method. 3.9 Simplex Algorithm. 3.10 Two Phases of the Simplex Method. 3.11 MATLAB Solution of LP Problems. References and Bibliography. Review Questions. Problems. 4 Linear Programming II: Additional Topics and Extensions. 4.1 Introduction. 4.2 Revised Simplex Method. 4.3 Duality in Linear Programming. 4.4 Decomposition Principle. 4.5 Sensitivity or Postoptimality Analysis. 4.6 Transportation Problem. 4.7 Karmarkar's Interior Method. 4.8 Quadratic Programming. 4.9 MATLAB Solutions. References and Bibliography. Review Questions. Problems. 5 Nonlinear Programming I: One-Dimensional Minimization Methods. 5.1 Introduction. 5.2 Unimodal Function. ELIMINATION METHODS. 5.3 Unrestricted Search. 5.4 Exhaustive Search. 5.5 Dichotomous Search. 5.6 Interval Halving Method. 5.7 Fibonacci Method. 5.8 Golden Section Method. 5.9 Comparison of Elimination Methods. INTERPOLATION METHODS. 5.10 Quadratic Interpolation Method. 5.11 Cubic Interpolation Method. 5.12 Direct Root Methods. 5.13 Practical Considerations. 5.14 MATLAB Solution of One-Dimensional Minimization Problems. References and Bibliography. Review Questions. Problems. 6 Nonlinear Programming II: Unconstrained Optimization Techniques. 6.1 Introduction. DIRECT SEARCH METHODS. 6.2 Random Search Methods. 6.3 Grid Search Method. 6.4 Univariate Method. 6.5 Pattern Directions. 6.6 Powell's Method. 6.7 Simplex Method. INDIRECT SEARCH (DESCENT) METHODS. 6.8 Gradient of a Function. 6.9 Steepest Descent (Cauchy) Method. 6.10 Conjugate Gradient (Fletcher-Reeves) Method. 6.11 Newton's Method. 6.12 Marquardt Method. 6.13 Quasi-Newton Methods. 6.14 Davidon-Fletcher-Powell Method. 6.15 Broyden-Fletcher-Goldfarb-Shanno Method. 6.16 Test Functions. 6.17 MATLAB Solution of Unconstrained Optimization Problems. References and Bibliography. Review Questions. Problems. 7 Nonlinear Programming III: Constrained Optimization Techniques. 7.1 Introduction. 7.2 Characteristics of a Constrained Problem. DIRECT METHODS. 7.3 Random Search Methods. 7.4 Complex Method. 7.5 Sequential Linear Programming. 7.6 Basic Approach in the Methods of Feasible Directions. 7.7 Zoutendijk's Method of Feasible Directions. 7.8 Rosen's Gradient Projection Method. 7.9 Generalized Reduced Gradient Method. 7.10 Sequential Quadratic Programming. INDIRECT METHODS. 7.11 Transformation Techniques. 7.12 Basic Approach of the Penalty Function Method. 7.13 Interior Penalty Function Method. 7.14 Convex Programming Problem. 7.15 Exterior Penalty Function Method. 7.16 Extrapolation Techniques in the Interior Penalty Function Method. 7.17 Extended Interior Penalty Function Methods. 7.18 Penalty Function Method for Problems with Mixed Equality and Inequality Constraints. 7.19 Penalty Function Method for Parametric Constraints. 7.20 Augmented Lagrange Multiplier Method. 7.21 Checking the Convergence of Constrained Optimization Problems. 7.22 Test Problems. 7.23 MATLAB Solution of Constrained Optimization Problems. References and Bibliography. Review Questions. Problems. 8 Geometric Programming. 8.1 Introduction. 8.2 Posynomial. 8.3 Unconstrained Minimization Problem. 8.4 Solution of an Unconstrained Geometric Programming Program Using Differential Calculus. 8.5 Solution of an Unconstrained Geometric Programming Problem Using Arithmetic-Geometric Inequality. 8.6 Primal-Dual Relationship and Sufficiency Conditions in the Unconstrained Case. 8.7 Constrained Minimization. 8.8 Solution of a Constrained Geometric Programming Problem. 8.9 Primal and Dual Programs in the Case of Less-Than Inequalities. 8.10 Geometric Programming with Mixed Inequality Constraints. 8.11 Complementary Geometric Programming. 8.12 Applications of Geometric Programming. References and Bibliography. Review Questions. Problems. 9 Dynamic Programming. 9.1 Introduction. 9.2 Multistage Decision Processes. 9.3 Concept of Suboptimization and Principle of Optimality. 9.4 Computational Procedure in Dynamic Programming. 9.5 Example Illustrating the Calculus Method of Solution. 9.6 Example Illustrating the Tabular Method of Solution. 9.7 Conversion of a Final Value Problem into an Initial Value Problem. 9.8 Linear Programming as a Case of Dynamic Programming. 9.9 Continuous Dynamic Programming. 9.10 Additional Applications. References and Bibliography. Review Questions. Problems. 10 Integer Programming. 10.1 Introduction 588. INTEGER LINEAR PROGRAMMING. 10.2 Graphical Representation. 10.3 Gomory's Cutting Plane Method. 10.4 Balas' Algorithm for Zero-One Programming Problems. INTEGER NONLINEAR PROGRAMMING. 10.5 Integer Polynomial Programming. 10.6 Branch-and-Bound Method. 10.7 Sequential Linear Discrete Programming. 10.8 Generalized Penalty Function Method. 10.9 Solution of Binary Programming Problems Using MATLAB. References and Bibliography. Review Questions. Problems. 11 Stochastic Programming. 11.1 Introduction. 11.2 Basic Concepts of Probability Theory. 11.3 Stochastic Linear Programming. 11.4 Stochastic Nonlinear Programming. 11.5 Stochastic Geometric Programming. References and Bibliography. Review Questions. Problems. 12 Optimal Control and Optimality Criteria Methods. 12.1 Introduction. 12.2 Calculus of Variations. 12.3 Optimal Control Theory. 12.4 Optimality Criteria Methods. References and Bibliography. Review Questions. Problems. 13 Modern Methods of Optimization. 13.1 Introduction. 13.2 Genetic Algorithms. 13.3 Simulated Annealing. 13.4 Particle Swarm Optimization. 13.5 Ant Colony Optimization. 13.6 Optimization of Fuzzy Systems. 13.7 Neural-Network-Based Optimization. References and Bibliography. Review Questions. Problems. 14 Practical Aspects of Optimization. 14.1 Introduction. 14.2 Reduction of Size of an Optimization Problem. 14.3 Fast Reanalysis Techniques. 14.4 Derivatives of Static Displacements and Stresses. 14.5 Derivatives of Eigenvalues and Eigenvectors. 14.6 Derivatives of Transient Response. 14.7 Sensitivity of Optimum Solution to Problem Parameters. 14.8 Multilevel Optimization. 14.9 Parallel Processing. 14.10 Multiobjective Optimization. 14.11 Solution of Multiobjective Problems Using MATLAB. References and Bibliography. Review Questions. Problems. A Convex and Concave Functions. B Some Computational Aspects of Optimization. B.1 Choice of Method. B.2 Comparison of Unconstrained Methods. B.3 Comparison of Constrained Methods. B.4 Availability of Computer Programs. B.5 Scaling of Design Variables and Constraints. B.6 Computer Programs for Modern Methods of Optimization. References and Bibliography. C Introduction to MATLAB(R) . C.1 Features and Special Characters. C.2 Defining Matrices in MATLAB. C.3 CREATING m-FILES. C.4 Optimization Toolbox. Answers to Selected Problems. Index .