Fall 2016
EE 236A
Christina Fragouli
Linear Programming
Homework 3
Due noon, Tuesday Oct. 18, 2016
Total points: 15
Problem 1 (3 points, Exer. 35 (a) in Linear Programming Exercises):
Is x
= (1, 1, 1, 1) an extreme point of the polyhedron P defined by th

Fall 2015
EE 236A
Christina Fragouli
Linear Programming
Homework 4
Due 08:10 am, Tuesday Oct. 27, 2014
Total points: 20
Problem 1 (4 points, Exer. 24 in Linear Programming Exercises):
Describe how you would use linear programming to solve the following pr

Fall 2015
EE 236A
Christina Fragouli
Linear Programming
Homework 1
Due 8:15am, Tuesday Oct. 6, 2015
Problem 1: A company produces products A, B, and C; and can sell them in unlimited quantities at
the following prices: A, $8; B, $65; C, $120. Producing a

Fall 2015
EE 236A
Christina Fragouli
Linear Programming
Homework 5
Due 08:10 am, Tuesday Nov. 17, 2015
Total points: 18
Problem 1 (4 points):
The following are the max-flow LP and the min-cut ILP formulations as weve seen in class and
the provided chapter

Fall 2015
EE 236A
Christina Fragouli
Linear Programming
Homework 5
Due 08:10 am, Tuesday Nov. 17, 2015
Total points: 18
Problem 1 (4 points):
The following are the max-flow LP and the min-cut ILP formulations as weve seen in class and
the provided chapter

Fall 2015
EE 236A
Christina Fragouli
Linear Programming
Homework 3
Due 08:10 am, Tuesday Oct. 20, 2014
Total points: 20 + 1
Problem 1 (4 points, Exer. 41 in Linear Programming Exercises):
Let P Rnn be a matrix with the following two properties:
all eleme

Fall 2015
EE 236A
Christina Fragouli
Linear Programming
Homework 6
Due 08:10 am, Tuesday Nov. 24, 2015
Total points: 18
Problem 1:
We consider the problem of multicasting information in communication networks. Given a source s
and a set of receivers R whe

Fall 2015
EE 236A
Christina Fragouli
Linear Programming
Solutions of Homework 2
Problem 1 (0.4 points): Linear programming models are used by many Wall Street firms to select
a desirable bond portfolio. The following is a simplified version of such a mode

Fall 2015
EE 236A
Christina Fragouli
Linear Programming
Homework 4
Due 08:10 am, Tuesday Oct. 27, 2014
Total points: 20
Problem 1 (4 points, Exer. 24 in Linear Programming Exercises):
Describe how you would use linear programming to solve the following pr

Fall 2015
EE 236A
Christina Fragouli
Linear Programming
Homework 2
Due noon, Tuesday Oct. 13, 2015
Problem 1 (0.4 points): Linear programming models are used by many Wall Street firms to select
a desirable bond portfolio. The following is a simplified ver

Fall 2015
EE 236A
Christina Fragouli
Linear Programming
Solutions of Homework 1
Problem 1: A company produces products A, B, and C; and can sell them in unlimited quantities at
the following prices: A, $8; B, $65; C, $120. Producing a unit of A requires 1

Fall 2015
EE 236A
Christina Fragouli
Linear Programming
Homework 6
Due 08:10 am, Tuesday Nov. 24, 2015
Total points: 18
Problem 1:
We consider the problem of multicasting information in communication networks. Given a source s
and a set of receivers R whe

Fall 2015
EE 236A
Christina Fragouli
Linear Programming
Homework 7
Due 8:10am, Tuesday Dec. 1, 2015
Problem 1 (4 points):
(a) Use the simplex procedure to solve the following problem
minimize z = x y
subject to x + y 2
x y 6
x, y 0.
(b) Draw a graphical r

Fall 2016
EE 236A
Christina Fragouli
Linear Programming
Homework 4
Due noon, Tuesday Oct. 25, 2016
Total points: 20
Problem 1 (4 points, Exer. 24 in Linear Programming Exercises):
Describe how you would use linear programming to solve the following proble

Fall 2015
EE 236A
Prof. Christina Fragouli
TA: Mohammed Karmoose
EE236A Linear Programming
Midterm Solutions
Thursday Oct. 29, 2015
Problem 1 (8 points): Consider the following optimization problem:
minimize cT x
subject to
0x1
(1)
with x Rn .
1. (3 point

Fall 2014
EE 236A
Prof. Christina Fragouli
TA: Linqi Song
EE236A Linear Programming
Midterm Solutions
Thursday Nov. 13, 2014
Problem 1 (8 points): Consider the following two LPs, with P1 :
minimize cT x
subject to Ax b,
(1)
maximize bT z
subject to AT z +

EE 236A, Fall 2016,
Professor: C. Fragouli,
SR: Yahya Essa
Class Logistics
Class website: https:/eeweb.ee.ucla.edu/grad/classinfo.php?/ee236A/1/fall/16. Please
check the website often: we will upload the homeworks there and later their solutions.
Profes

L. Vandenberghe
EE236A (Fall 2013-14)
Lecture 6
Duality
dual of an LP in inequality form
variants and examples
complementary slackness
61
Dual of linear program in inequality form
we define two LPs with the same parameters c Rn, A Rmn, b Rm
an LP in i

EE236A: Linear Programming
Fall 2016
Tuesday, November 29th
Lecturer: Martina Cardone & Christina Fragouli
Submodular functions are a relevant class of set-functions, which can be used to model practical problems
in several areas of computer science and a

Massachusetts Institute of Technology
18.433: Combinatorial Optimization
Michel X. Goemans
Handout 3
February 9th, 2009
1. Lecture notes on bipartite matching
Matching problems are among the fundamental problems in combinatorial optimization.
In this set

L. Vandenberghe
EE236A (Fall 2013-14)
Lecture 2
Piecewise-linear optimization
piecewise-linear minimization
1- and -norm approximation
examples
modeling software
21
Linear and affine functions
linear function: a function f : Rn R is linear if
f (x + y

L. Vandenberghe
EE236A (Fall 2013-14)
Lecture 1
Introduction
course overview
linear optimization
examples
history
approximate syllabus
basic definitions
linear optimization in vector and matrix notation
halfspaces and polyhedra
geometrical interpreta

L. Vandenberghe
EE236A (Fall 2013-14)
Lecture 3
Polyhedra
linear algebra review
minimal faces and extreme points
31
Subspace
definition: a nonempty subset S of Rn is a subspace if
x, y S,
, R
=
x + y S
extends recursively to linear combinations of more

Fall 2015
EE 236A
Christina Fragouli
Linear Programming
Homework 3
Due 08:10 am, Tuesday Oct. 20, 2014
Problem 1 (4 points, Exer. 41 in Linear Programming Exercises): Let P Rnn be a matrix with
the following two properties:
all elements of P are nonnegat