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National Taiwan Normal University Course Outline Spring , 2021 |
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| I.Course information |
| Serial No. | 2645 | Course Level | |
| Course Code | MAC0144 | Chinese Course Name | 非線性規劃（二） |
| Course Name | Nonlinear Programming (II) | ||
| 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 | Mon. 6-8 Gongguan 11111 | ||
| 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 | ||
| Schedule | |||
延續非線性規劃（I），本課程將對各種(無約束條件與具有約束條件)的最佳化問題的解的存在性與相關的演算法之理論部分作詳細的介紹，整體來說將涵蓋凸分析知識、Karush-Kuhn-Tucker定理、解存在性的限制資格(constraint qualification)、對偶定理(Duality theorem)、Quasi-Newton method、BFGS、Conjugate gradient、Barrier method、Penalty method、Proximal point method等各種演算法。 |
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| Instructional Approach | |||
| Methods | Notes | ||
| 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。 | ||
| Other: | 專題討論(對特定主題邀請相關學者專家進一步講授，以增進學生對課程內容之瞭解。) | ||
| Grading assessment | |||
| Methods | Percentage | Notes | |
| Assignments | 30 % | 指定論文、補充材料的閱讀。 | |
| Class discussion involvement | 20 % | 出席並參與課堂討論、聆聽相關研討會演講的情形。 | |
| Presentation | 50 % | 輪流上台報告所研讀的內容對培養研究生作研究的態度與能力是非常重要的，因此將針對每位學生上台報告的講解中，評量其對研讀內容的理解程度。 | |
| Required and Recommended Texts/Readings with References | There are four references for this course. We will mainly use the first one in this semester. 1. Nonlinear Programming, 3rd edition, by D.P. Bertsekas, 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 IRn , by L. D. Berkovitz, 2002. 4. Numerical Optimization, by J. Nocedal and S. Wright, 2006.
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