Course Name: Optimization Methods

Course Code: S2293027

Semester: 3

Credit: 2

Program: Electronics

Course Module: Compulsory

Responsible: Qijun Zhang, Yan Xu

E-mail:qjz@doe.carleton.ca

Department:Tianjin International Engineering Institute, Tianjin University

TimeAllocation(1 credit hour = 45 minutes)

Course Description

The course takes a unified view of optimization and covers the main areas of application and the main optimization algorithms. It covers the following topics:

• Linear optimization

• Robust optimization

• Network flows

• Discrete optimization

• Dynamic optimization

• Nonlinear optimization

Prerequisite

Mathematics, Probability, Linear Algebra.

Course Objectives

This course introduces the principal algorithms for linear, network, discrete, robust, nonlinear, dynamic optimization and optimal control, and emphasizes methodology and the underlying mathematical structures. Topics include the simplex method, network flow methods, branch, bound and cutting plane methods for discrete optimization, optimality conditions for nonlinear optimization, interior point methods for convex optimization, Newton's method, heuristic methods, and dynamic programming and optimal control methods.

Course Syllabus

1. Linear optimization

   1. Applications of linear optimization

   2. Geometry of linear optimization

   3. Simple method

   4. Duality theory

   5. Sensitivity analysis

2. Robust optimization

   1. Robust optimization

   2. Large scale optimization

3. Network flows

4. Discrete optimization

   1. Applications of discrete optimization

   2. Branch and bound and cutting planes

   3. Lagrange an methods

   4. Heuristics and approximation algorithms

5. Dynamic programming

6. Nonlinear optimization

   1. Applications of nonlinear optimization

   2. Optimality conditions and gradient methods

   3. Line searches and Newton's method

   4. Conjugate gradient methods

   5. Affine scaling algorithm

   6. Interior point methods

Textbooks & References

Textbook:

• Bertsimas, Dimitris, and John Tsitsiklis.Introduction to Linear Optimization. Belmont, MA: Athena Scientific, 1997. ISBN: 9781886529199.

We may also use readings from a few textbooks:

• Stephen Boyd and Lieven Vandenberghe.Convex Optimization. Cambridge University Press, 2009.

Grade Distribution

Total Grades:100%

Capability Tasks

CT1: To understand basic science, and to have analytical ability and the ability to integrate related knowledge.

CT2: To apply relevant professional knowledge to the field of science and technology: understanding of the basic concepts and its connotation, application of different methods and concepts which have been learned, capability of judging the scope and limitations of such applications.

CT3: To grasp methodologies and engineering tools: identifying, utilizing and solving problems. Even if the students are not familiar with the content, they can turn to computer tools for systematic analysis.

CT4: To carry out experiments in research environment with the abilities to utilize tools, especially for data collection and processing.

CT10: To have the capacity to work in international environment; the capability to master one or more foreign languages and be open to foreign cultures; be able to acclimatize themselves to the international language environment.

Achievements

• To be able to build and improve a model, and to apply this model to practice. - Level: M

• To make the link between various systems and optimization approaches or schemes. - Level: M

• To be able to extract and propose an optimization issue for a practical engineering problem. - Level: A

Students: Electronics, Year 2