Optimization Methods for Engineers

Catalog description

This course is designed to help the interested engineering students to develop working knowledge of optimization and, specifically, to develop the skills and background needed to recognize, formulate, and solve convex optimization problems. Convex optimization problems emerge naturally in the design and analysis of systems across the entire engineering spectrum. First, the course will briefly review basic concepts of linear algebra and calculus. Second, students will be introduced to optimization (problem formulation, feasibility sets, etc.) and principles of convexity, including convex functions, convex sets, convex problems and properties thereof. Then, an array of algorithmic numerical methods will be studied for the solution of convex problems, covering, among other topics, gradient methods, coordinate descent, Lagrangian duality, saddle points, optimality conditions etc. Last, the course will focus on how to formulate and solve convex problems in engineering, including convex approximation of non-convex problems and regularization. Many practical application examples will be studied from diverse areas of engineering. Through a series of assignments and in-class examples, students will learn how to practically solve optimization problems in MATLAB, using state-of-the-art toolboxes.