Title of the course: Introcduction to Convex Optimization
Instructor: MSc. Oğuzhan Yürük
Institution: Technische Universität Berlin
Dates: 10-16 September 2018
Prerequisites: Basic Linear Algebra
Level: Advanced undergraduate, beginning Undergraduate
Abstract: This will be an introductory course on convex optimization. Participants are expected to have a basic knowledge of linear algebra. A background on optimization is not required however it can be useful. The main goal of this course is to provide participants with the required understanding of convex optimization in order to study conic programming. During the 6 days we will cover the following:
• Day 1: The notation that will be used throughout the course will be set. Preliminary results coming from the linear algebra will be given
• Day 2: The notions of affine hull, convex hull and conic hull will be introducted and we will see the Carathedory’s theorem on convex hulls.
• Day 3: We will cover the operations that preserve convexity. Then we will prove an important result of convexity, seperating hyperplane theorem.
• Day 4: Definition of a convex function and operations that preserve convex functions will be given. The first and second order convexity conditions for functions will be shown and used to verify some important examples of convex functions.
• Day 5: The notion of convex optimization problem will be introduced with the notation that comes with it. First order optimality conditions will be proven.
• Day 6: We will focus on generalized cone inequalities and then understand what is a conic programming problem why it is a convex problem.