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課程名稱 |
數值優化
Numerical Optimization |
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開課學期 |
105-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
薛克民 |
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課號 |
MATH5414 |
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課程識別碼 |
221 U5700 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期二8,9(15:30~17:20)星期四5(12:20~13:10) |
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上課地點 |
天數302天數302 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1052MATH5414_nopt201 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Topics (tentative) to be discussed include:
1. Unconstrained minimization
2. Constrained minimization
3. Special topics
(a) Nonlinear least squares
(b) Global optimization
(c) Optimization for differential equations
Applications of the described numerical optimization methods will be given to problems
arising from signal processing, inverse design, and others, see the website:
http://www.ceremade.dauphine.fr/~peyre/numerical-tour/tours/#optim
for an example. |
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課程目標 |
本課程之目標為:
1. 講授基本的數值最佳化方法: 它的建構過程與理論基礎,
2. 數值驗證最佳化方法之理論行為與應用. |
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課程要求 |
先修課程: Numerical linear algebra, or its equivalence |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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參考書目 |
1. J. Nocedal and S. J. Wright, Numerical Optimization, 2nd [electronic
resource], Springer, 2006.
2. I. Griva, S.G. Nash, A. Sofer, Linear and Nonlinear Optimization
[electronic resource], 2nd, SIAM 2009.
3. S. Boyd and L. Vandenberghe, Convex Optimization, Combridge 2009 (Web ebook).
4. M.C. Ferris, O.L. Mangasarian, S.J. Wright, Linear Programming with Matlab,
SIAM 2007.
5. J.E. Dennis, Jr., Robert B. Schnabel, Numerical methods for unconstrained
optimization and
nonlinear equations [electronic resource], SIAM 1996. |
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指定閱讀 |
L1 magic note (see bulletin board) |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Homework |
60% |
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2. |
Midterm exam |
20% |
Time: 15:30-17:20, 04/18, 2017, open book and note |
3. |
Final exam |
20% |
Time: 15:30-17:20, 06/20, 2017, open book and note |
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週次 |
日期 |
單元主題 |
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第18週 |
06/20 |
Final exam |
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第1-1週 |
02/21 |
Course overview, examples, &
Newton's method for unconstrained optimization |
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第1-2週 |
02/23 |
Unconstrained optimization: Line search methods |
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第2-2週 |
02/28 |
No class: National holiday |
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第2-2週 |
03/02 |
Unconstrained optimization: Trust region methods |
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第3-2週 |
03/09 |
Unconstrained optimization: Quasi-Newton methods |
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第4-2週 |
03/16 |
Optimization problems with equality constraints |
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第6-1週 |
03/28 |
Optimization problems with inequality constraints |
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第7-1週 |
04/04 |
No class: National holiday |
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第8-2週 |
04/13 |
Non-smooth optimization: Convex case |
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第9-1週 |
04/18 |
Midterm exam |
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第9-2週 |
04/20 |
Subgradient of convex function |
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第10-1週 |
04/25 |
Convex programming: ISTA |
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第10-2週 |
04/27 |
Proximal gradient methods (E. Candes's note posted in bulletin board) |
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第11-1週 |
05/02 |
Convex programming: FISTA |
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第12-1週 |
05/09 |
No class: Self-learning week begin |
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第12-2週 |
05/11 |
No class: Self-learning week end |
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第13-1週 |
05/16 |
Bregman & split Bregamn algorithms |
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第13-2週 |
05/18 |
Singular value thresholding (SVT) for matrix completion problems |
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第14-2週 |
05/25 |
Robust PCA |
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第15-1週 |
05/30 |
No class: National holiday |
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第16-1週 |
06/06 |
Semi-definite programming (SDP) |
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