Tom Luo
Lecture 0: Introduction and overview
Course outline
some general features of convex optimization
example
duality example
what we will/wont do
how many problems are convex?
prerequisites
1
Tom Luo
Course topics
Tentative Course Outline:
1.
Convex Optimization
Z.-Q. Luo
01/25/2016
Homework Assignment #1 (Due: Feb 1, 4:00 pm in class)
1. Show that the convex hull H of a set S is the intersection D of all convex sets D that
contain S. (The same method can be used to show that the conic, or ane
Convex Optimization
Z.-Q. Luo
01/25/2016
Homework Assignment #1 (Due: Feb 1, 4:00 pm in class)
1. Show that the convex hull H of a set S is the intersection D of all convex sets D that
contain S. (The same method can be used to show that the conic, or ane
EE 8950
Tom Luo
Lecture 8: Sequential unconstrained minimization
brief history of SUMT & IP methods
logarithmic barrier function
central path
UMT & SUMT
complexity analysis
feasibility phase
generalized inequalities
1
EE 8950
Tom Luo
History of SUM
EE 8950
Tom Luo
Lecture 7: Smooth unconstrained minimization
terminology
general descent method
gradient & steepest descent methods
Newtons method
quasi-Newton methods
conjugate gradients
self-concordance & Newtons method
1
EE 8950
Tom Luo
Terminol
EE 8950
Tom Luo
Lecture 4: Linear and quadratic problems
linear programming
examples and applications
linear fractional programming
quadratic optimization problems
(quadratically constrained) quadratic programming
second-order cone programming
exam
EE 8950
Tom Luo
Lecture 5: Geometric and semidenite programming
geometric programming
geometric programming in convex form
applications
semidenite programming
applications
1
EE 8950
Tom Luo
Geometric programming
monomial function:
f (x) = cx1 1 x2 2
EE 8950
Tom Luo
Lecture 3: Convex optimization problems
optimization problem in standard form
convex optimization problem
standard form with generalized inequalities
multicriterion optimization
1
EE 8950
Tom Luo
Optimization problem: standard form
min
Tom Luo
Lecture 0: Introduction and overview
Course outline
some general features of convex optimization
example
duality example
what we will/wont do
how many problems are convex?
prerequisites
1
Tom Luo
Course organization
course website (lecture
EE8239
T. Luo
2/16/2017
Homework Assignment #4 Extra Problem
1. SINR maximization. We consider n transmitters with powers p1 , . . . , pn
0, transmitting to n receivers. These powers are the optimization variables in the problem. We let G Rnn denote the
First Order Methods for Large Scale Optimization
Zhi-Quan Luo
Department of Electrical and Computer Engineering
University of Minnesota
30 March 2014
First Order Methods
Zhi-Quan Luo
Lecture 1: Issues of Large Scale Optimization
Motivating examples:
comp
EE 8950
Tom Luo
Ellipsoid Method
idea of localization methods
bisection on R
center of gravity algorithm
ellipsoid method
1
EE 8950
Tom Luo
Localization
f : Rn R convex (and for now, differentiable)
problem: minimize f
oracle model: for any x we ca
EE8231
T. Luo
2/1/16
Homework Assignment #2 (Due Feb 8, 4:00 pm in class)
1. Exercise 2.33 The monotone and monotone nonnegative cone. We dene the monotone
cone as
Km = cfw_x Rn |x1 x2 xn ,
i.e., all vectors with components in sorted order. We dene the mo