最优化理论是应用的原版教材“Introduction to optimization”，教学方式采用双语教学。本课程包含无约束最优化基础，常规线性搜索方法，无约束最优化算法如梯度法、牛顿法、拟牛顿法，线性规划如单纯型法以及修正单纯型法，线性约束最优化基础，非线性最优化方法如罚函数法，Lagrange 乘子法等。本课程先行课程需要数学分析、高等代数、矩阵理论、谱理论、计算方法等。考核方式为闭卷考试。
考核方式：选择百分制，期末考试70%、课程作业10%、上课（缺席、迟到等）20%。
数学分析、高等代数、矩阵理论、谱理论、计算方法等。
2.Real vector spaces and matrices (2hrs)
3.Transformations(1hrs)
3.1 Linear transformation
3.2 △Eigenvalues and eigenvectors
3.3 Orthogonal projections
3.4 △Quadratic forms
3.5 Matrix norms
4. Concepts from geometry (2hrs)
4.1 Line segments
4.2 ★Hyperplanes and linear varieties
4.3 Convex sets
4.4 Neighborhoods
4.5★ Polytopes and polyhedra
5. Elements of differential calculus (2hrs)
5.1 Differentiability
5.2 The derivative matrix
5.3 Chain rule
5.4△ Level sets and gradients
5.5 △Taylor series
6. Basics of unconstrained optimization (2hrs)
6.1 Introduction
6.2 ★Conditions for local minima
7.one-demensional search methods (3hrs)
7.1 Golden section search
7.2 Fibonacci search
7.3 ★Newton’s method
7.4 Secant method
7.5 Remarks on line search methods
8.Gradient methods (5hrs)
8.1 Introduction
8.2 ★Steepest descent method
8.3 △Analysis of gradient methods
9. Newton’s method (2hrs)
9.1 Introduction
9.2 △★Analysis of Newton’s method
10. Conjugate direction methods (6hrs)
10.1 Introduction
10.2 △The conjugate direction algorithm
10.3 △The conjugate gradient algorithm
10.4 The conjugate gradient algorithm for nonquadratic problems
11. Quasi-Newton methods (6hrs)
11.1 Introduction
11.2△ ★Approximating the inverse Hessian
11.3 ★The rank one correction formula
11.4 ★The DFP algorithm
11.5 ★The BFGS algorithm
13 Introduction to linear programming (5hrs)
13.1 A brief history of linear programming
13.2 △Simple example of linear programs
13.3 △Two-dimensional linear programs
13.4 Convex polyhedra and linear programming
13.5★ Standard-form linear programs
13.6 ★Basic solutions
13.7 ★Properties of basic solutions
13.8 A geometric view of linear programs
14. The simplex method (7hrs)
14.1 Solving linear equations using row operation
14.2 ★The canonical augmented matrix
14.3★ Updating the augmented matrix
14.4 ★The simplex algorithm
14.5 Matrix form of the simplex method
14.6★ The two-phase simplex method
14.7 ★The revised simplex method
17. Problems with equality constraints (6hrs)
17.1 Introduction
17.2 Problem formulation
17.3 △Tangent and normal spaces
17.4△ Lagrange conditions
17.5 △Second-order conditions
18. Problems with inequality (5hrs)
18.1★ Karush kuln tucker conditions
18.2 ★Second-order conditions
19. Algorithms for constrained optimization (5hrs)
19.1 ★Projected gradient methods
19.2 ★Penalty methods
20.The developments of optimization (5hrs)
[1]袁亚湘，孙文瑜著，最优化理论与方法，科学出版社，2003.04。
[2]Jorge Nocedal, Stephen J. Wright, Numerical Optimization（数值最优化），科学出版社，2006.01（影印版）。