This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include the simplex method, network flow methods, branch and 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.
The course aims at integrating traditional design methodologies with concepts and techniques of modern optimization theory and practice. In the course the student will learn to create an appropriate mathematical description (a simulation model) of the design problem, to formulate the optimization problem and finally to use numerical optimization techniques and computer support tools in order to solve the problem. The course has an emphasis on system design where “design" is defined in a broad context, and therefore students from diverse disciplines are welcome to attend the course.
Course Learning Outcomes
Upon completion of this course, students will:
• Demonstrate knowledge and understanding of the basic ideas underlying optimization techniques;
• Demonstrate knowledge and understanding of some of the most common standard optimization models and how they can be solved;
• Appreciate some of the power of using the mathematical approach to optimization problems relevant to engineering;
• Show logical thinking in problem solving;
• Develop mathematical optimization models for a range of practical problems;
• Formulate large-scale Linear and Integer Programming problems, input a problem into a computer efficiently, and then solve the problem.
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