Nonlinear Optimization
CO 367 Winter 2014
Homework 2
Due Jan 30, 2014
Reading: Read Chapter 1 and start on Chapter 3 of the textbook.
Please explain your answers and proofs carefully. A yes or no does not constitute a valid answer;
nor does a numerical va

C&O 367 - Winter 2013 Midterm
Page 1
UNIVERSITY OF WATERLOO
MIDTERM EXAMINATION
WINTER 2013
Surname:
First Name:
Id.#:
Course
Course Title
Instructor
Date of Exam
Time Period
Number of Exam Pages
(including this cover sheet)
Exam Type
Additional Instructi

C&O367: Nonlinear Optimization
(Winter 2013)
Assignment 2
H. Wolkowicz
Posted ?
Due: Thursday, Jan. 31, 10:00AM (before class),
1
Convex Sets
1.1
Intersection of Convex Sets
Show that the intersection of convex sets is a convex set. Is the union of convex

C&O367: Nonlinear Optimization
(Winter 2013)
Assignment 4
H. Wolkowicz
Posted Mon, Feb. 8
Due: Thursday, Feb. 28 10:00AM (before class),
1
Matrices
1.1
Positive Denite Matrices
1. Let A S n , i.e., let A be a symmetric, real n n matrix. Show that A 0 if,

CO367: Nonlinear Optimization
Lecture 9, Tues Feb. 5, 2013.
Lecturer: Henry Wolkowicz
text: The Mathematics of Nonlinear Programming, [1],
at Dept. Combinatorics and Optimization, University of Waterloo
February 6, 2013
Iterative Methods for Unconstrained

CO367: Nonlinear Optimization
Lecture 8, Thursday Jan. 31, 2013.
Henry Wolkowicz
Dept. Combinatorics and Optimization, University of Waterloo
February 1, 2013
Denition: f : D R, D Rn open convex set
f is a convex function iff
1
(0-order: secant lines lie

C&O367: Nonlinear Optimization
(Winter 2013)
Assignment 5
H. Wolkowicz
Posted Monday, Mar. 4
Due: Thursday, Mar. 19 10:00AM (before class)
1
Hyperplanes
1.1
Separating Hyperplanes
First we recall some denitions:
(a) K is a cone if K K, 0;
(b) K is a conve

CO 351: Assignment 5
Due Thursday, July 24, in class
Assignment Policy: While it is acceptable for students to discuss the course material and
the assignments, the work you hand in should be your own and in your own words. Outright
copying is a very serio

CO 351: Assignment 6
Due Thursday, July 24, in class
Assignment Policy: While it is acceptable for students to discuss the course material and
the assignments, the work you hand in should be your own and in your own words. Outright
copying is a very serio

CO 351: Assignment 5
Due Thursday, July 17, in class
Assignment Policy: While it is acceptable for students to discuss the course material and
the assignments, the work you hand in should be your own and in your own words. Outright
copying is a very serio

1. We will use Corollary 1 from the lecture notes to solve this problem. That is, if x is a
local minimizer of a C 2 -smooth function f : (a, b) R, then f (x) = 0 and f (x) 0.
Using this result, we will nd the potential candidates for local minimizers. Ho

Nonlinear Optimization
CO 367 Winter 2014
Homework 1
Due Jan 16, 2014
Please explain your answers and proofs carefully. A yes or no does not constitute a valid
answer; nor does a numerical value with no explanation constitute a valid answer.
1. (2 points)

Nonlinear Optimization
CO 367 Winter 2014
Scribe: Dmitriy Drusvyatskiy
Lecture 2
Jan 9, 2014
Lecture 2: Unconstrained Optimization continued
We begin with the simplest situation: no constraints and a function of a single variable. How
can we recognize a m

Nonlinear Optimization
CO 367 Winter 2014
Scribe: Tara Munikar
Lecture 5
Jan 21, 2014
Lecture 5: Directions of descent
We nished the last lecture with the following theorem.
Theorem 1 (Directions of descent) Suppose f : Rn R is C 2 -smooth. Then for any
v

Nonlinear Optimization
CO 367 Winter 2014
Scribe: Michael Lee Baker
Lecture 3
Jan 14, 2014
Lecture 3: Unconstrained optimization continued
Theorem 1 (Multivariate optimality conditions) Let f : U R be C 2 -smooth on an
open set U in Rn . Then the followin

Nonlinear Optimization
CO 367 Winter 2014
Scribe: Johannes Ackermann
Lecture 4
Jan 16, 2014
Lecture 4: Introduction to iterative methods for unconstrained optimization
Recall: We are interested in nding a minimizer of a C 2 -smooth function f : Rn R.
The

Nonlinear Optimization
CO 367 Winter 2014
Scribe: Dmitriy Drusvyatskiy
Lecture 1
Jan 7, 2014
Information about the lectures:
Instructor: Dmitriy Drusvyatskiy (MC 4012), [email protected]
TA: Ahmad Abdi
Webpage: learn.uwaterloo.ca
Textbook: The Mat

Review Assignment 0
Due Tuesday, May 13, in class
Assignment Policy: While it is acceptable for students to discuss the course material and
the assignments, the work you hand in should be your own and in your own words. Outright
copying is a very serious

CO 351: Assignment 1
Due Thursday, May 22, in class
Assignment Policy: While it is acceptable for students to discuss the course material and
the assignments, the work you hand in should be your own and in your own words. Outright
copying is a very seriou

CO 351: Assignment 2 Solutions
Q1. Let D = (N, A) be a digraph with node s N , where all nodes can be reached from s. Take
arbitrary weights w RA and feasible potentials y RN . The reduced weights w RA are
dened as follows:
wuv = wuv + yu yv
uv A.
Observe

CO 351: Assignment 2
Due Thursday, June 5, in class
Assignment Policy: While it is acceptable for students to discuss the course material and
the assignments, the work you hand in should be your own and in your own words. Outright
copying is a very seriou

CO 351: Assignment 3
Due Thursday, June 19, in class
Assignment Policy: While it is acceptable for students to discuss the course material and
the assignments, the work you hand in should be your own and in your own words. Outright
copying is a very serio

CO 351: Assignment 4
Due Thursday, July 3, in class
Assignment Policy: While it is acceptable for students to discuss the course material and
the assignments, the work you hand in should be your own and in your own words. Outright
copying is a very seriou