|
National Taiwan Normal University Course Outline Fall , 2023 |
|
@尊重智慧財產權,請同學勿隨意影印教科書 。 Please respect the intellectual property rights, and shall not copy the textbooks arbitrarily. |
|
| I.Course information |
| Serial No. | 2632 | Course Level | Master / PhD |
| Course Code | MAC0143 | Chinese Course Name | 非線性規劃（一） |
| Course Name | Nonlinear Programming (I) | ||
| Department | Department of Mathematics | ||
| Two/one semester | 1 | Req. / Sel. | Sel. |
| Credits | 3.0 | Lecturing hours | Lecture hours: 3 |
| Prerequisite Course | ◎1. This is a cross-level course and is available for junior and senior undergraduate students, master's students and PhD students. 2. If the listed course is a doctroal level course, it is only available for master's students and PhD students. | ||
| Comment | |||
| Course Description | |||
| Time / Location | Tue. 6-8 Gongguan M212 | ||
| Curriculum Goals | Corresponding to the Departmental Core Goal | ||
| 1. Understand the theoretical background of various optimization problems |
Master: 1-1 Equipped with professional mathematics competences Doctor: 1-1 Equipped with professional mathematics competences |
||
| 2. Understand algorithms for solving various optimization problems |
Master: 1-2 Being able to reason and induct with mathematical logic 1-3 Being able to think mathematically and critically 1-4 Possessing the abilities to propose and solve questions in advanced mathematics Doctor: 1-2 Being able to reason and induct with mathematical logic 1-3 Being able to think mathematically and critically 1-4 Possessing the abilities to propose and solve questions in advanced mathematics |
||
| 3. Learn about practical applications of various optimization problems |
Master: 1-5 Being able to use mathematics as tools to learn other subjects Doctor: 1-5 Being able to use mathematics as tools to learn other subjects |
||
| II. General Syllabus |
| Instructor(s) | CHEN, Jein-Shan/ 陳界山 | ||
| Schedule | |||
本課程主要在研究各種非線性規劃問題的極小值問題，內容包括解的存在性與相關的演算法。本課程將從介紹凸分析知識出發，對無約束條件的最佳化問題與具有約束條件的最佳化問題，分別講授其相關的理論背景，再介紹其常用的演算法。 Nonlinear programming deals with the problem of optimizing an objective function in the presence of equality and inequality constraints. If all the functions are linear, it is called a linear program; oththerwise, the problem is called nonlinear program. The course focuses on background materials, study of solutions existence, and the design of solutions methods/algorithms for nonlinear programs. The good news is that there are no homework and exams for this course. However, this is a graduate course, so you are highly expected to show your ability for independent study. Instead of assigning weekly homework or taking exams, I will arrange everyone who enrolls in this course to take turns presenting course materials. Hopefully, you will learn more through this training. |
|||
| Instructional Approach | |||
| Methods | Notes | ||
| Formal lecture | |||
| Group discussion | 每個選修此課程的學生將被指定研讀的章節，並輪流上台報告所研讀的內容。 | ||
| Grading assessment | |||
| Methods | Percentage | Notes | |
| Class discussion involvement | 20 % | Discussions (輪流上台報告所研讀的內容) | |
| Attendances | 30 % | Attendance (參加研討會、出席課堂討論) | |
| Presentation | 50 % | Presentations (輪流上台報告所研讀的內容) | |
| Required and Recommended Texts/Readings with References | 1. Nonlinear Programming, by D.P. Bertsekas, 3rd edition, Athena Scientific, 2016. 2. Nonlinear Programming: Theory and Algorithms, 3rd edition, by M. Bazaraa, H. Sherali, and C. Shetty, 2006. 3. Convexity and Optimization in R^n, by L. D. Berkovitz, 2002. 4. Numerical Optimization, by J. Nocedal and S. Wright, 2006. |
||