Course Description

There are two questions to be addressed in this course. First, given an optimization problem in hand, how can we reformulate it, or well approximate it, into a tractable convex problem, allowing the adoption of abundant convex optimization theories (e.g., Karush-Kuhn-Tucker theory) to obtain a stable (and hopefully closed-form) solution? Second, given a large-scale (reformulated/approximated) convex problem in hand, how can we solve it with suitable optimization methods (e.g., Fast Proximal Gradient Method (FPGM) and Alternating Direction Method of Multipliers (ADMM)), that guarantee both convergence and computational efficiency? Addressing these two questions, equipping course attendees with fundamental knowledges in convex optimization (a new degree of freedom for solving cutting-edge research problems), demonstrating real-world applications in remote sensing and related areas, as well as introducing off-the-shelf convex optimization software, are the objectives of this course.

Course Objectives

1. Understand the basic concepts of convex optimization and convex geometry.

2. Master the skill of reformulating an optimization problem as a convex problem.

3. Be able to customize an efficient algorithm for your convex problem.