最佳化理論

臺北科技大學 114-2 學期課程，課號 356914。

課程大綱

本課程將會介紹「非限制最佳化問題、線性規劃、非線性限制最佳化問題」。這些問題將會由數學推導與MATLAB模擬得到解決。對於解決非限制最佳化問題，一維搜尋法、梯度法、牛頓共軛方向法、擬牛頓法會將在本課程介紹及使用；線性規劃問題會利用單形法來解決；拉格朗日及KKT乘數則用來解決非線性限制最佳化問題。 Course Description：In this course, unconstrained optimization problems, linear programming, and nonlinear constrained optimization problems are presented. Mathematical derivations and MATLAB simulations are used to analyze and obtain the solutions to these problems. For unconstrained optimization problems, one-dimensional search, gradient, Newton's, conjugate direction, quasi-Newton methods are presented. For linear programming problems, simplex method is introduced. Last, Lagrange and Karush-Kuhn-Tucker multipliers are presented for solving nonlinear constrained optimization problems.

課程進度

1. 02/26 INTRODUCTION 2. 03/05 MATHEMATICAL REVIEW 3. 03/12 UNCONSTRAINED OPTIMIZATION- Basics of Set-Constrained and Unconstrained Optimization 4. 03/19 UNCONSTRAINED OPTIMIZATION-One-Dimensional Search Methods 5. 03/26 UNCONSTRAINED OPTIMIZATION-One-Dimensional Search Methods 6. 04/02 UNCONSTRAINED OPTIMIZATION-One-Dimensional Search Methods 7. 04/09 UNCONSTRAINED OPTIMIZATION-One-Dimensional Search Methods 8. 04/16 UNCONSTRAINED OPTIMIZATION-Gradient Methods 9. 04/23 Midterm Exam 10. 04/30 UNCONSTRAINED OPTIMIZATION-Gradient Methods 11. 05/07 UNCONSTRAINED OPTIMIZATION-Newton's Method 12. 05/14 UNCONSTRAINED OPTIMIZATION-Newton's Method 13. 05/21 UNCONSTRAINED OPTIMIZATION-Conjugate Direction Methods 14. 05/28 UNCONSTRAINED OPTIMIZATION-Conjugate Direction Methods 15. 06/04 LINEAR PROGRAMMING 16. 06/11 LINEAR PROGRAMMING 17. 06/18 Paper Presentation 18. 06/25 Paper Presentation PS: The contents will be adjusted according to actual needs

評量方式

- Class participation: 15% - Assignments: 30% (No assignment turned in late will be accepted) - Midterm exam: 25% - Paper Presentation: 30%

教材

【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】 使用外文原文書：是 1. An Introduction to Optimization, 4th Edition, Edwin K. P. Chong, Stanislaw H. Zak, WILEY, 2013. 2. Optimization Concepts and Applications in Engineering (3rd ed.). Belegundu, A., & Chandrupatla, T., Cambridge: Cambridge University Press. 2019.