In this course, we will mainly teach the theory and methods to solve the optimization problems. The following is the plan of the teaching:

First week. Introduction of the optimization problems and the backgroud knowledge.

Second week. The theory and application of the simplex algorithm.

Third week. Dual simplex algorithm and the integer programming.

Fourth week. Line search and KKT condition.

Fifth week. The gradient-based methods of the unconstrained optimization problems.

Sixth week. Heuristic methods.

Siventh week. Using python and Matlab to solve the optimization problems.

Eighth week. Review of the course. 

Jan A. Snyman, Practical Mathematical Optimization, Springer Press, 2005

Jorge Nocedal, Stephen J. Wright, Numerical Optimization, Springer Press, 2006

Wenyu Sun, Ya-Xiang Yuan, Optimization Theory and Methods, Springer Press, 2006

George Dantzig,  Linear Programming and Extensions. Princeton, NJ: Princeton University Press, 1963.

Baolin Chen, Optimization Theory and Algorithms, Tsinghua University Press, 2005.

David G. Luenberger and Yinyu Ye, Linear and nonlinear programming, Springer, 2007.

Stephen G. Nash and Ariela Sofer, Linear and nonlinear programming, The McGraw-Hill Companies, Inc., 1996.

Dimitri P. Bertsekas, Nonlinear Programming, Athena Scientific, 1999.

Stephen Boyd and Lieven Vandenberghe, Convex optimization, Cambridge University Press, 2004. 

G. Hadley, Linear programming, Addison-Wesley publishing company, 1963. 

Y. Ye, Interior point algorithms, theory and analysis, John Wiley & Sons, New York, 1997

J. F. Bonnans et al, Numerical optimization: theoretical and practical aspects, Universitext, Springer, Berlin, 2003. 

There are a lot mathematical software can be used to solve the optimization problem, such as MATLAB, R, Excel, and Python.

For MATLAB, we refer to the website: https://www.mathworks.com/.

More reference books will be provided later here. 

For R, we refer to the homepage: https://www.r-project.org/.

We highly recommend the students go to the website of Python to download the Python:  https://www.python.org/.

For the reference books, we refer to Chapter 10 in the course. 

This course is a very important course for the graduate students in Hohai university. It has great application in civil engineering, traffic problem, water conservancy, geophysics, management science, finance theory, social sciences. In this course, we will mainly introduce the theory and methods to solve the optimization problems. We will show the methods to solve the linear programming problems such as the simplex algorithm, the methods to do the line search, the gradient-based methods to solve the unconstrained optimization problems, KKT condition of the constrained optimization problems. In addition, we also talk about the heuristic methods. In the meantime, we also show how to use the mathematical sofeware such as MATLAB, Python to solve the optimization problems.