Applied Optimization: Formulation and Algorithms for Engineering Systems (Hardcover)
暫譯: 應用優化:工程系統的模型與演算法 (精裝版)

Ross Baldick

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Description

The starting point in the formulation of any numerical problem is to take an intuitive idea about the problem in question and to translate it into precise mathematical language. This book provides step-by-step descriptions of how to formulate numerical problems so that they can be solved by existing software. It examines various types of numerical problems and develops techniques for solving them. A number of engineering case studies are used to illustrate in detail the formulation process. The case studies motivate the development of efficient algorithms that involve, in some cases, transformation of the problem from its initial formulation into a more tractable form. Five general problem classes are considered: linear systems of equations, non-linear systems of equations, unconstrained optimization, equality constrained optimization, and inequality constrained optimization. The book contains many worked examples and homework exercises and is suitable for students of engineering or operations research taking courses in optimization. For appendices, teaching materials, and Instructor's solutions for homework exercises in the book, please follow the 'resources and solutions' link on this page.

Uses case studies to illustrate formulation of problems, emphasizing problem features such as monotonicity, convexity, symmetry, and sparsity ¿ Large number of homework exercises and worked examples: solution set available for instructors. ¿ Two appendices, of mathematical preliminaries and of proofs, available for downloading

 

Table of Contents

1. Introduction; 2. Problems, algorithms, and solutions; 3. Transformation of problems; Part I. Linear Simultaneous Equations: 4. Case studies; 5. Algorithms; Part II. Non-linear Simultaneous Equations: 6. Case studies; 7. Algorithms; 8. Solution of the case studies; Part III. Unconstrained Optimization: 9. Case studies; 10. Algorithms; 11. Solution of the case studies; Part IV. Equality Constrained Optimization: 12. Case studies; 13. Algorithms for linear constraints; 14. Algorithms for non-linear constraints; Part V. Inequality Constrained Optimization: 15. Case studies; 16. Algorithms for non-negativity constraints; 17. Algorithms for linear constraints; 18. Solution of the case studies; 19. Algorithms for non-linear constraints; 20. Solution of the case studies; References; Index.

商品描述(中文翻譯)

**描述**

任何數值問題的形成起點是對所討論問題的直觀理解,並將其轉化為精確的數學語言。本書提供了逐步描述如何形成數值問題,以便可以通過現有軟體進行求解。它考察了各種類型的數值問題並發展了解決這些問題的技術。書中使用了多個工程案例研究來詳細說明形成過程。這些案例研究激勵了高效算法的開發,在某些情況下,這涉及將問題從其初始形成轉化為更易處理的形式。考慮了五個一般問題類別:線性方程組、非線性方程組、無約束優化、等式約束優化和不等式約束優化。本書包含許多已解題例和作業練習,適合修習優化課程的工程或運籌學學生。關於附錄、教學材料和本書作業練習的教師解答,請參閱本頁的「資源與解答」連結。

使用案例研究來說明問題的形成,強調問題特徵,如單調性、凸性、對稱性和稀疏性。大量的作業練習和已解題例:解答集可供教師使用。兩個附錄,數學初步知識和證明,可供下載。

**目錄**

1. 介紹;2. 問題、算法與解答;3. 問題的轉化;第一部分:線性聯立方程:4. 案例研究;5. 算法;第二部分:非線性聯立方程:6. 案例研究;7. 算法;8. 案例研究的解答;第三部分:無約束優化:9. 案例研究;10. 算法;11. 案例研究的解答;第四部分:等式約束優化:12. 案例研究;13. 線性約束的算法;14. 非線性約束的算法;第五部分:不等式約束優化:15. 案例研究;16. 非負約束的算法;17. 線性約束的算法;18. 案例研究的解答;19. 非線性約束的算法;20. 案例研究的解答;參考文獻;索引。