Utah State University
Department of Electrical and Computer Engineering
ECE 6040 Convex Optimization - Fall 2017
Schedule
Week 1
Monday 8/28/2017
introduction to the course, policies, etc.
description of lines and hyperplanes
combinations: linear, affine, conic, convex
Wednesday 8/30/2017
three representations of hyperplanes
graphical solution to linear programming problem
combinations: linear, affine, conic, convex
Friday 9/1/2017
affine hull, conic hull, convex hull
affine sets, cones, convex cones, convex sets
interior and relative interior of a set
convex objects: hyperplane, subspace, halfspace, slab, norm ball
Week 2
Wednesday 9/6/2017
operations that preserve convexity: intersections; images and inverse images under affine transformations, perspective transformations, linear fractional functions; and projection onto some coordinates
inverse image examples
separating hyperplane theorem
Friday 9/8/2017
applications of the separating hyperplane theorem
theorems of the alternative
supporting hyperplanes
supporting hyperplane theorem
Week 3
Watch Boyd's lecture 3 (convex functions) online
Friday 9/15/2017
Taylor approximation of differentiable functions
Summary of convex functions
Definition of convex functions
Week 4
Monday 9/18/2017
First order condition for convexity
Second order condition for convexity
Examples of convex functions
Wednesday 9/20/2017
Sublevel sets and convexity
Graphs, epigraphs, hypographs, level sets
Supporting hyperplane theorem and epigraphs of convex functions
Jensen's inequality
Maximization and convexity
Friday 9/22/2017
Compositions and examples
Minimization and examples
Perspective function
Introduction to conjugate functions
Week 5
Monday 9/25/2017
Conjugate function definition and interpretation
Procedure for computing conjugage functions
Examples of conjugate functions
Wednesday 9/27/2017
Friday 9/29/2017
Convexit with respect to generalized inequalities
Convexity on a line, first order condition
Introduction to constrained optimization problems
Terminology (optimum value, optimum point, active/inactive constraints, unbounded below, unattained, etc.)