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.
Language: EN