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課程名稱 |
數值優化
Numerical Optimization |
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開課學期 |
101-2 |
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授課對象 |
理學院 數學系 |
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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 |
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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 |
星期一7,8(14:20~16:20)星期三7(14:20~15:10) |
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上課地點 |
天數201天數201 |
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備註 |
總人數上限：30人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1012nopt2012 |
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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 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: 它的理論基礎與``收斂''性質,
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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指定閱讀 |
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參考書目 |
1. J. Nocedal and S. J. Wright, Numerical Optimization, 2nd [electronic resource],
Springer, 2006.
2. J.F. Bonnans, J.C. Gilbert, C. Lemarechal, and C.A. Sagastizabal, Numerical
Optimization:Theoretial and Practical Aspects, 2nd, Springer, 2006 (book is
available on web).
3. J.E. Dennis, Jr., Robert B. Schnabel, Numerical methods for unconstrained
optimization and nonlinear equations [electronic resource], SIAM 1996.
4. C. R. Vogel, Computational Methods for Inverse Problems [electronic
resource], SIAM 2002.
5. R. Fletcher, Practical Methods of Optimization, 2nd, Wiley 2000.
6. I. Griva, S.G. Nash, A. Sofer, Linear and Nonlinear Optimization
[electronic resource], 2nd, SIAM 2009.
7. M.C. Ferris, O.L. Mangasarian, S.J. Wright, Linear Programming with Matlab,
SIAM 2007. |
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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 |
50% |
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2. |
Term project |
50% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/18,2/20 |
Course overview & some examples |
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第2週 |
2/25,2/27 |
No class (out of town for a conference) |
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第3週 |
3/04,3/06 |
Unconstrained optimization:
Newton \& quasi-Newton methods |
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第4週 |
3/11,3/13 |
Trust-region methods |
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第5週 |
3/18,3/20 |
Trust-region methods & least squares problems |
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第6週 |
3/25,3/27 |
Conjugate gradient methods |
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第7週 |
4/01,4/03 |
Large-scale unconstrained optimization |
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第8週 |
4/08,4/10 |
Computing derivatives;
Term project proposal |
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第9週 |
4/15,4/17 |
Derivative-free optimization |
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第10週 |
4/22,4/24 |
Theory of constrained optimization |
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第11週 |
4/29,5/01 |
Linear programming: Simplex method |
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第13週 |
5/13,5/15 |
Linear programming: Interior-point methods |
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第14週 |
5/20,5/22 |
Quadratic programming |
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第17週 |
6/10,6/12 |
Project presentation |
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