This course builds the ability of recognizing and solving convex optimization problems that arise in applications.
Contents are as follow:
First, Convex sets, functions, and optimization problems.
Second, Basics of convex analysis.
Third, Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems.
Forth, Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods.
Last, Applications to signal processing, statistics and machine learning, control and mechanical engineering, digital and analog circuit design, and finance.
Textbook: Convex Optimization, Stephen Boyd and Lieven Vandenberghe