ENGG 5501: Foundations of Optimization
201617 First Term
Handout 2: Elements of Convex Analysis
Instructor: Anthony ManCho So
September 12, 2016
As briefly mentioned in Handout 1, the notion of convexity plays a very important role in both
the theoretical

ENGG 5501: Foundations of Optimization
201617 First Term
Homework Set 4
Instructor: Anthony ManCho So
Due: November 21, 2016
SOLVE THE FOLLOWING PROBLEMS:
n , , . . . , > 0, and , . . . , > 0 be given. Consider
Problem 1 (25pts). Let A1 , . . . , Am S+
1

ENGG 5501: Foundations of Optimization
201617 First Term
Handout 3: Elements of Linear Programming
Instructor: Anthony ManCho So
1
October 8, 2015
Basic Definitions and Properties
We now turn to the study of a very important class of optimization problems

ENGG 5501: Foundations of Optimization
201617 First Term
Homework Set 3
Instructor: Anthony ManCho So
Due: October 31, 2016
SOLVE THE FOLLOWING PROBLEMS:
Problem 1 (25pts). Consider a production game defined as follows. Let N = cfw_1, . . . , n be
the set

ENGG 5501: Foundations of Optimization
201617 First Term
Handout 6: Some Applications of Conic Linear Programming
Instructor: Anthony ManCho So
1
October 31, 2016
Introduction
Conic linear programming (CLP), and in particular, semidefinite programming (SD

ENGG 5501: Foundations of Optimization
201617 First Term
Handout 5: Elements of Conic Linear Programming
Instructor: Anthony ManCho So
1
October 19, 2016
Introduction
As we saw in the previous handout, linear programming is a powerful tool for modelling a

ENGG 5501: Foundations of Optimization
201617 First Term
Homework Set 1
Instructor: Anthony ManCho So
Due: September 30, 2016
SOLVE THE FOLLOWING PROBLEMS:
cfw_
Problem 1 (20pts). Let P = x Rn : aTi x bi for i = 1, . . . , m , where a1 , . . . , am Rn an

ENGG 5501: Foundations of Optimization
201617 First Term
Homework Set 2
Instructor: Anthony ManCho So
Due: October 14, 2016
SOLVE THE FOLLOWING PROBLEMS:
Problem 1 (15pts). Let f : R2 R cfw_+ be the function given by
0
if k(x1 , x2 )k2 < 1,
[0, +] if k(x

ENGG 5501: Foundations of Optimization
201617 First Term
Handout 1: Introduction
Instructor: Anthony ManCho So
1
September 5, 2016
Basic Notions in Optimization
In this course we will consider a class of mathematical programming problems that can be
expre

ENGG 5501: Foundations of Optimization
201617 First Term
Handout 4: Some Applications of Linear Programming
Instructor: Anthony ManCho So
1
October 12, 2016
Introduction
The theory of LP has found many applications in various disciplines. In this lecture,