必修課程介紹

• 預備知識：微積分、線性代數
• 適合年級： 研究生
• 課程簡介：

介紹線性規劃的背景由來、數學模型、與其幾類求解線性規劃的方法。

• 課程大綱：

1. Introduction
2. Geometry of Linear Programming
3. The Revised Simplex Method
4. Duality Theory and Sensitivity Analysis
5. Complexity Analysis and the Ellipsoid Method
6. Karmarkar's Projective Scaling Algorithm
7. Affine Scaling Algorithms
8. Insights into the Interior-Point Methods
9. Affine Scaling for Convex Quadratic Programming
10. Implementation of Interior-Point Algorithms

• 參考書目：

1. S.-C. Fang and S. Puthenpura, Linear Optimization and Extensions: Theory and Algorithms, AT&T - Prentice-Hall, Englewood Cliffs, NJ, 1993.
2. M.S. Bazaraa, H.D. Sherali, and C.M. Shetty, Nonlinear programming: theory and algorithms (3rd ed.), Wiley, New York, 2006.