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National Taiwan Normal University Course Outline Fall , 2025 |
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| I.Course information |
| Serial No. | 2591 | Course Level | Master / PhD |
| Course Code | MAC0081 | Chinese Course Name | 優選理論專題（一） |
| Course Name | Topics in Optimization Theory (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 | |||
| Day & Class Period/Location | Tue. 6-8 Gongguan M212 | ||
| Curriculum Goals | Corresponding to the Departmental Core Goal | ||
| 1. Understand the structure of general mathematical programming problems. |
Master: 1-1 Equipped with professional mathematics competences Doctor: 1-1 Equipped with professional mathematics competences |
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| 2. Be familiar with various preferred or optimized conditions. |
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 various related applications. |
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 | ||
| Schedule | |||
This semester, we will focus on a theme -- Numerical Optimization, which contains the following contents: 1. Foundamentals of Unconstrained Optimization 2. Line Search Methods 3. Trust-Region Methods 4. Conjugate Gradient Methods 5. Quasi-Newton Methods 6. Large-Scale Unconstrained Optimization 7. Derivative-Free Optimization 8. Least-Squares Problems 9. Nonlinear Equations 10. Theory of Constrained Optimization 11. Foundamentals of Algorithms for Nonlinear Constrained Optimization 12. Quadratic Programming 13. Penalty and Augmented Lagrangian Methods 14. Sequential Quadatic Programming 15. Interior-Point Methods |
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| Instructional Approach | |||
| Methods | Notes | ||
| Group discussion | Students enrolled in this course will take turn doing presentations. | ||
| Case studies | Sometimes students will be asked to attend conferences or workshops related to this course. | ||
| Grading assessment | |||
| Methods | Percentage | Notes | |
| Class discussion involvement | 20 % | Discussions | |
| Attendances | 30 % | Attendance | |
| Presentation | 50 % | Presentations | |
| Required and Recommended Texts/Readings with References | 1. Numerical Optimization, J. Nocedal and S. J. Wright, Springer Series in Operations Research, 2006. |
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