Introduction to Convex Optimization Theory

This course focuses on the theory and applications and algorithms of convex optimization. It focuses on recognizing and solving convex optimization problems that arise in many engineering fields. It is divided into three parts; Mathematical background, convex optimization theory, and its applications. The Mathematical background part reviews relevant topics in linear Algebra that are necessary for the students to complete the course. The theory part covers the basics of convex analysis and convex optimization problems such as linear programming (LP), semi-definite programming (SDP), second order cone programming (SOCP), and geometric programming (GP), as well as duality in general convex and conic optimization problems. The third part of the course focuses on engineering applications of convex optimization, from systems and control theory to estimation, data fitting, and information theory.