Optimization Theory and Applications
Time: 6-17 weeks D2216, Thirsday 4:15-6:00 pm and Friday 2:00-3:45 pm
Outline
- Chapter 1 Introduction to Optimization
- Overview of optimization
- Examples of optimization problems
- Mathematical models and classifications of optimization problems
- Introduction to Matlab optimization toolbox
- Chapter 2 Preliminary Knowledges
- Notations
- Vector Space and Matrix
- Geometry
- Chapter 3 Unconstrained Optimization Problem
- Introduction
- Conditions for local minimizers
- Chapter 4 One-dimensional Search Methods
- Golden section search
- Fibonacci search
- Bisection method
- Secant method
- Bracketing
- Chapter 5 Gradient Methods
- Method of Steepest Descent
- Analysis of Optimization Algorithms
- Analysis of Gradient Methods
- Chapter 6 Newton’s Method
- Analysis of Newton’s Method
- Modification of Newton’s Method
- Chapter 7 Conjugate Direction Methods
- Conjugate Vectors
- Conjugate Gradient Algorithm
- Chapter 8 Quasi-Newton Methods
- Quasi-Newton Algorithm
- Rank One Algorithm
- DFP Algorithm
- BFGS Algorithm
- Chapter 9 Linear Programming
- Brief history of linear programming
- Simple examples of linear programs
- Standard form linear programs
- Basic solutions
- Application examples of linear programming
- Chapter 10 Integer Programming
- Prototype example
- Some BIP applications
- Branch and bound method
- Application examples of integer programming
- Chapter 11 Equality Constrained Nonlinear Programming
- Basics of nonlinear programming
- Equality constraints
- The theorem of Lagrange
- Second-order conditions
- Chapter 12 Inequality Constrained Nonlinear Programming
- The theorem of Karush-Kuhn-Tucker
- Using KKT conditions
- Application examples ( Water Filling Algorithm by Peiling Hou in Nov. 2022)
- Chapter 13 Convex Optimization
- Introduction to optimization
- Convex functions
- Convexity and optimization
- Application examples of convex optimization
- Chapter 14 Application: Max-Flow-Min-Cut
- Reading Session
- Presentation