課程名稱 |
凸函數最佳化 Convex Optimization |
開課學期 |
112-2 |
授課對象 |
電機工程學研究所 |
授課教師 |
蔡坤諭 |
課號 |
CommE5050 |
課程識別碼 |
942EU0640 |
班次 |
01 |
學分 |
3.0 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期四2,3,4(9:10~12:10) |
上課地點 |
電二101 |
備註 |
本課程以英語授課。 總人數上限:25人 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
課程大綱
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課程概述 |
[Course description]
Mathematical optimization has pervasive applications in not only almost all natural science and engineering disciplines such as electrical engineering (especially in control, communication, signal processing, and electronic design automation), computer science, and operations research, just to name a few, but also social sciences such as economics. Among various types of optimization problems, convex optimization problems are special in that they can be solved very efficiently, and thus they have gained much attention. Moreover, many optimization problems fall into this broad category. For instances, linear least squares, linear programming, quadratic programming, geometric programming, and semidefinite programming are special cases of convex optimization.
The importance of convex optimization is becoming more and more apparent as there are many more emerging scientific and engineering problems being solved efficiently in this manner. This course primarily focuses on developing students’ capability of recognizing and formulating convex optimization problems arising from their own research fields, and when time permits, it also introduces how such problems are solved and applied. Students are also encouraged to develop heuristic approaches based on convex optimization theory and techniques to tackle general nonlinear, nonconvex optimization problems encountered in their fields of interest.
[Course topics]
1. Introduction to convex optimization
2. Convex sets
3. Convex functions
3. Convex optimization problems
4. Duality theory (optimality conditions; sensitivity analysis)
5. Algorithms* (descent methods; Newton's method; interior-point methods)
6. Applications* (approximation and fitting, statistical estimation, etc.) |
課程目標 |
[Course goals]
Basic:
- Recognize/formulate some engineering problems as convex optimization problems
- Utilize or develop code to solve CVX optimization problems
- Characterize optimal solution (e.g. limits of performance)
Bonus:
- Advance your own research work at NTU
- Develop good presentation and technical writing skills in English
- Develop heuristic approaches based on convex optimization to tackle general nonlinear, nonconvex optimization problems |
課程要求 |
[Prerequisites]
Calculus (esp. Lagrange multiplier), linear algebra (esp. linear least squares and singular value decomposition) |
預期每週課後學習時數 |
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Office Hours |
備註: (appointments by email) |
指定閱讀 |
[BV04] S. Boyd and L. Vandenberghe, Convex Optimization |
參考書目 |
[Ber99] D. P. Bertsekas, Nonlinear Programming, 2nd ed.
[Ven01] P. Venkataraman, Applied Optimization with Matlab Programming
[BSS06] M. S. Bazaraa, M. D. Sherali, and C. M. Sherali, Nonlinear
Programming, 3rd ed.
[LY08] D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming |
評量方式 (僅供參考) |
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針對學生困難提供學生調整方式 |
上課形式 |
以錄影輔助 |
作業繳交方式 |
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考試形式 |
書面(口頭)報告取代考試 |
其他 |
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週次 |
日期 |
單元主題 |
Week 1 |
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Course info. and Introduction |
Week 3 |
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Convex sets |
Week 4 |
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Convex functions |
Week 5 |
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Convex optimization problems |
Week 6 |
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Duality (I) |
Week 8 |
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Duality (II) |
Week 10 |
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Unconstrained minimization*; Equality-constrained minimization* |
Week 11 |
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Final project proposal presentation (Final project proposal due) |
Week 12 |
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Interior-point methods* |
Week 13 |
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Approximation and fitting* |
Week 14 |
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Statistical estimation* |
Week 15 |
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Geometric problems* |
Week 16 |
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Summary and Review; Techniques for Non-convex problems* |
Week 17 |
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Final exam |
Week 18 |
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Final project report/presentation 1st version due (present in class) (Final-exam week) 10% penalty/work day; last grade submission: 6/17 |
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