一、課程說明(Course Description)
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<br>Numerical optimization concerns the computations of the maximum (or the 
<br>minimum) of differentiable functions which can have one or several variables, 
<br>with or without constraints.  Important classes in the numerical optimization 
<br>problems include linear programming, unconstrained optimization, and nonlinear 
<br>programming.  This course will study the numerical algorithms and the 
<br>theoretical background for each problem.  Applications that motivate the 
<br>computation will be mentioned as well.
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<br>二、指定用書(Text Books)
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<br>J. Nocedal and S. Wright, Numerical Optimization, Springer Verlag 1999
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<br>三、參考書籍(References)
<br>1. Stephen G. Nash and Ariela Sofer, Linear and Nonlinear Programming, 1996
<br>2. J. Dennis and R. Schnabel, Numerical Methods for Unconstrained Optimization 
<br>and Nonlinear Equations, (republished by) SIAM (Classics in Applied Mathematics 
<br>16) 1996
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<br>四、教學方式(Teaching Method)
<br>Most of time will be lecturing. 
<br>Project and paper presentation will be held if time permit.
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<br>五、教學進度(Syllabus)
<br>1.	Introduction. 
<br>2.	Linear programming
<br>	2.1.	Geometry interpretation and properties
<br>	2.2.	The simplex method
<br>	2.3.	Duality, sensitivity, and complexity
<br>	2.4.	Practical concerns
<br>3.	Unconstrained optimization
<br>	3.1.	Optimality condition
<br>	3.2.	Newton’s method
<br>	3.3.	Line search method
<br>	3.4.	Trust-Region method
<br>	3.5.	Practical concerns
<br>4.	Constrained programming
<br>	4.1.	Lagrange multiplier and KKT conditions.
<br>	4.2.	Feasible direction method
<br>	4.3.	Penalty and Augmented Lagrange method.
<br>	4.4.	Interior point methods
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<br>六、成績考核(Evaluation)
<br>1. Class notes (50)
<br>2. Project (50)
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<br>七、可連結之網頁位址
<br>http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html
<br>http://www-unix.mcs.anl.gov/otc/Guide/faq/nonlinear-programming-faq.html
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