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)
<br>None
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<br>三、參考書籍(References)
<br>1. Applied Optimization with Matlab Programming, 2nd Ed, P. Venkataraman (Class 
<br>page) (Companion site)
<br>2. Numerical optimization, Jorge Nocedal and Stephen J. Wright 
<br>(http://www.mcs.anl.gov/otc/Guide)
<br>3. Afternotes on Numerical Analysis, G.W. Stewart link
<br>4. Mathematical Optimization, MO
<br>5. Linear and Nonlinear Programming, Stephen G. Nash and Ariela Sofer (1996, 
<br>2005)
<br>6. Numerical Methods for Unconstrained Optimization and Nonlinear Equations, J. 
<br>Dennis and R. Schnabel
<br>7. Matrix computations, 3rd Ed, Gene Howard Golub and Charles F. Van Loan (1996)
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<br>四、教學方式(Teaching Method)
<br>Lecture presentation.
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<br>五、教學進度(Syllabus)
<br>1. Background introduction.
<br>   1.1 One variable optimization
<br>   1.2 Linear algebra
<br>2. Unconstrained optimization
<br>   2.1  Optimality condition
<br>   2.2  Newton’s method
<br>   2.3	Line search method
<br>   2.4	Trust-Region method
<br>   2.5	Practical concerns
<br>3. Linear programming
<br>   3.1	Geometry interpretation and properties
<br>   3.2.	The simplex method
<br>   3.3.	Duality, sensitivity, and complexity
<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
<br>5. Other topics
<br>   5.1 Discrete optimization
<br>   5.2 Global optimization
<br>   5.3 Integer programming
<br>   5.4 Mixed integer programming
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<br>六、成績考核(Evaluation)
<br>1. Midterm (30)
<br>2. Final or project (30)
<br>3. Homework (30)
<br>4. Attendance (10)
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