Applied Optimization: Formulation and Algorithms for Engineering Systems (Hardcover)

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.

《描述》

任何數值問題的制定起點是對問題有直觀的理解，並將其轉化為精確的數學語言。本書提供了逐步描述如何制定數值問題，以便可以通過現有軟件解決。它檢視了各種類型的數值問題並開發了解決它們的技巧。使用多個工程案例詳細說明了制定過程。這些案例激發了開發高效算法的動力，有時需要將問題從初始制定轉化為更易處理的形式。本書考慮了五個一般的問題類別：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。本書包含許多實例和作業練習，適合修讀優化課程的工程或運籌學學生。有關附錄、教學資料和本書作業練習的解答，請點擊本頁面上的“資源和解答”鏈接。

利用案例研究來說明問題的制定，強調問題的特徵，如單調性、凸性、對稱性和稀疏性。大量的作業練習和實例：教師可獲得解答集。兩個附錄，分別是數學初步知識和證明，可供下載。

《目錄》

1. 引言；2. 問題、算法和解決方案；3. 問題的轉化；第一部分 線性聯立方程組：4. 案例研究；5. 算法；第二部分 非線性聯立方程組：6. 案例研究；7. 算法；8. 案例研究的解決方案；第三部分 無約束優化：9. 案例研究；10. 算法；11. 案例研究的解決方案；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. 案例研究的解決方案；19. 非線性約束的算法；20. 案例研究的解決方案；參考文獻；索引。