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National Taiwan Normal University Course Outline Spring , 2026 |
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| I.Course information |
| Serial No. | 2572 | Course Level | Master / PhD |
| Course Code | MAC0082 | Chinese Course Name | 優選理論專題（二） |
| Course Name | Topics in Optimization Theory (II) | ||
| 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 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 | |||
No textbook required. Students who enroll in this course will take 1. First-Order Methods in optimization, by Amir Beck, MOS-SIAM Series on Optimization, 2017. 2. Optimization For Machine Learning, by S. Sra, S. Nowozin, and S. Wright, The MIT Press, 2012.
凸包、多面體、極端點、子梯度的性質。 優選條件與對偶性的介紹 對偶理論(Duality theory)。 網路優選與非線性規劃（網路流程、凸二次規劃、凸規劃、非凸規劃、幾何規劃、分式規劃及線性互補問題之優選條件及其求解法）。 |
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| Instructional Approach | |||
| Methods | Notes | ||
| Group discussion | Enrolled students will take turns to do presentations. | ||
| Other: | Sometimes guest speakers will be invited to deliver talks in this course. | ||
| Grading assessment | |||
| Methods | Percentage | Notes | |
| Class discussion involvement | 20 % | Attendance and Discussion are important parts of this course | |
| Attendances | 30 % | Attendance and Discussion are important parts of this course. | |
| Presentation | 50 % | regular presentations | |
| Adjustment methods for students | |||
| Required and Recommended Texts/Readings with References | First-Order Methods in optimization, by Amir Beck, MOS-SIAM Series on Optimization, 2017. Optimization For Machine Learning, by S. Sra, S. Nowozin, and S. Wright, The MIT Press, 2012. |
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