Course Syllabus

Course Information：

Year-Semester Course Number Course Name Phase Credits Hours Required/Elective Instructor Class Student NO. Withdraw Note

Spring Semester
Year 2024 329048 Introduction to Optimization 1 3.0 3 ★ Nien-Tsu Hu GAT
DME
機電外國學生專班 11 1 自動化所、機電博和機電博外生班合開合開

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Spring Semester Year 2024	329048	Introduction to Optimization	1	3.0	3	★	Nien-Tsu Hu	GAT DME 機電外國學生專班	11	1	自動化所、機電博和機電博外生班合開合開

Course Plan：

Instructor Nien-Tsu Hu　Office Hours

Email nthu@ntut.edu.tw

Last Updated 2024-05-15 17:00:00

Course Objective 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.

Course Schedule 1. 02/21 Introduction 2. 02/28 Legal Holiday 3. 03/06 MATHEMATICAL REVIEW 4. 03/13 UNCONSTRAINED OPTIMIZATION- Basics of Set-Constrained and Unconstrained Optimization 5. 03/20 UNCONSTRAINED OPTIMIZATION-One-Dimensional Search Methods 6. 03/27 UNCONSTRAINED OPTIMIZATION-One-Dimensional Search Methods 7. 04/03 UNCONSTRAINED OPTIMIZATION-One-Dimensional Search Methods 8. 04/10 UNCONSTRAINED OPTIMIZATION-Gradient Methods 9. 04/17 Midterm Exam 10. 04/24 UNCONSTRAINED OPTIMIZATION-Gradient Methods 11. 05/01 UNCONSTRAINED OPTIMIZATION-Newton's Method 12. 05/08 UNCONSTRAINED OPTIMIZATION-Newton's Method 13. 05/15 UNCONSTRAINED OPTIMIZATION-Conjugate Direction Methods 14. 05/22 UNCONSTRAINED OPTIMIZATION-Conjugate Direction Methods 15. 05/29 LINEAR PROGRAMMING 16. 06/05 LINEAR PROGRAMMING 17. 06/12 Paper Presentation 18. 06/19 Paper Presentation PS: The contents will be adjusted according to actual needs

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

Materials All right reserved. Do not reproduce without permission.

Foreign-language textbooks:Yes
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.

The access to curricular consultation TEL: (02)27712171 Ext. 4324
Email: nthu@ntut.edu.tw
Office Hours:
Tuesday 10:00-17:00
Integrate Technology Complex, Room 604-1

The course corresponds to the SDGs

Note
Weeks 17 and 18 will be performed via Microsoft Teams, if required (see https://news.ntut.edu.tw/p/422-1000-1085.php?Lang=zh-tw).

Instructor	Nien-Tsu Hu　Office Hours
Email	nthu@ntut.edu.tw
Last Updated	2024-05-15 17:00:00
Course Objective	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.
Course Schedule	1. 02/21 Introduction 2. 02/28 Legal Holiday 3. 03/06 MATHEMATICAL REVIEW 4. 03/13 UNCONSTRAINED OPTIMIZATION- Basics of Set-Constrained and Unconstrained Optimization 5. 03/20 UNCONSTRAINED OPTIMIZATION-One-Dimensional Search Methods 6. 03/27 UNCONSTRAINED OPTIMIZATION-One-Dimensional Search Methods 7. 04/03 UNCONSTRAINED OPTIMIZATION-One-Dimensional Search Methods 8. 04/10 UNCONSTRAINED OPTIMIZATION-Gradient Methods 9. 04/17 Midterm Exam 10. 04/24 UNCONSTRAINED OPTIMIZATION-Gradient Methods 11. 05/01 UNCONSTRAINED OPTIMIZATION-Newton's Method 12. 05/08 UNCONSTRAINED OPTIMIZATION-Newton's Method 13. 05/15 UNCONSTRAINED OPTIMIZATION-Conjugate Direction Methods 14. 05/22 UNCONSTRAINED OPTIMIZATION-Conjugate Direction Methods 15. 05/29 LINEAR PROGRAMMING 16. 06/05 LINEAR PROGRAMMING 17. 06/12 Paper Presentation 18. 06/19 Paper Presentation PS: The contents will be adjusted according to actual needs
Evaluation and grading policy	-Class participation: 15% - Assignments: 30% (No assignment turned in late will be accepted) - Midterm exam: 25% - Paper Presentation: 30%
Materials	All right reserved. Do not reproduce without permission. Foreign-language textbooks:Yes 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.
The access to curricular consultation	TEL: (02)27712171 Ext. 4324 Email: nthu@ntut.edu.tw Office Hours: Tuesday 10:00-17:00 Integrate Technology Complex, Room 604-1
The course corresponds to the SDGs
Note	Weeks 17 and 18 will be performed via Microsoft Teams, if required (see https://news.ntut.edu.tw/p/422-1000-1085.php?Lang=zh-tw).