Numerical optimization concerns the computations of the maximum (or the

minimum) of differentiable functions which can have one or several variables,

with or without constraints. Important classes in the numerical optimization

problems include linear programming, unconstrained optimization, and nonlinear

programming. This course will study the numerical algorithms and the

theoretical background for each problem. Applications that motivate the

computation will be mentioned as well.

二、指定用書(Text Books)

None

三、參考書籍(References)

1. Applied Optimization with Matlab Programming, 2nd Ed, P. Venkataraman (Class

page) (Companion site)

2. Numerical optimization, Jorge Nocedal and Stephen J. Wright

(http://www.mcs.anl.gov/otc/Guide)

3. Afternotes on Numerical Analysis, G.W. Stewart link

4. Mathematical Optimization, MO

5. Linear and Nonlinear Programming, Stephen G. Nash and Ariela Sofer (1996,

2005)

6. Numerical Methods for Unconstrained Optimization and Nonlinear Equations, J.

Dennis and R. Schnabel

7. Matrix computations, 3rd Ed, Gene Howard Golub and Charles F. Van Loan (1996)

四、教學方式(Teaching Method)

Lecture presentation.

五、教學進度(Syllabus)

1. Background introduction.

1.1 One variable optimization

1.2 Linear algebra

2. Unconstrained optimization

2.1 Optimality condition

2.2 Newton’s method

2.3 Line search method

2.4 Trust-Region method

2.5 Practical concerns

3. Linear programming

3.1 Geometry interpretation and properties

3.2. The simplex method

3.3. Duality, sensitivity, and complexity

4. Constrained programming

4.1. Lagrange multiplier and KKT conditions.

4.2. Feasible direction method

4.3. Penalty and Augmented Lagrange method.

4.4. Interior point methods

5. Other topics

5.1 Discrete optimization

5.2 Global optimization

5.3 Integer programming

5.4 Mixed integer programming

六、成績考核(Evaluation)

1. Midterm (30)

2. Final or project (30)

3. Homework (30)

4. Attendance (10)