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National Taiwan Normal University Course Outline Fall , 2026 |
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| I.Course information |
| Serial No. | 2665 | 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 |
| Teach in English | Y | Teach in National Languages | |
| 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 | |||
| Day & Class Period/Location | Tue. 6-8 Gongguan M211 | ||
| 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 |
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| 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 |
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| 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 |
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| II. General Syllabus |
| Instructor(s) | CHEN, Jein-Shan/ 陳界山 張毓麟 CHANG, Yu-Lin | ||
| 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. There are five references for this course. We will mainly read the first one in this semester. 1. Lectures on Nonsmooth Optimization, by Qinian Jin, Texts in Applied Mathematics, vol. 82, Springer, 2025. 2. Nonlinear Programming, by D.P. Bertsekas, 3rd edition, Athena Scientific, 2016. 3. Nonlinear Programming: Theory and Algorithms, 3rd edition, by M. Bazaraa, H. Sherali, and C. Shetty, 2006. 4. Convexity and Optimization in $\R^n$, by L. D. Berkovitz, 2002. 5. Numerical Optimization, by J. Nocedal and S. Wright, 2006. The good news is that there will be no homework assignments or examinations for this course. However, as this is a graduate-level course, you are expected to demonstrate a strong ability for independent study. Instead of weekly homework or exams, all enrolled students will take turns presenting the course materials. Through this process, I hope that you will develop a deeper understanding of the subject and benefit substantially from this form of academic training. |
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| Instructional Approach | |||
| Methods | Notes | ||
| Formal lecture | All enrolled students will take turns presenting the course materials. | ||
| Group discussion | All enrolled students will take turns presenting the course materials. | ||
| 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) | |
| Adjustment methods for students | |||
| Required and Recommended Texts/Readings with References | 1. Lectures on Nonsmooth Optimization, by Qinian Jin, Texts in Applied Mathematics, vol. 82, Springer, 2025. 2. Nonlinear Programming, by D.P. Bertsekas, 3rd edition, Athena Scientific, 2016. 3. Nonlinear Programming: Theory and Algorithms, 3rd edition, by M. Bazaraa, H. Sherali, and C. Shetty, 2006. 4. Convexity and Optimization in $\R^n$, by L. D. Berkovitz, 2002. 5. Numerical Optimization, by J. Nocedal and S. Wright, 2006. |
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