Math 171A: Mathematical Programming
Instructor: Philip E. Gill
Winter Quarter 2009
Homework Assignment #2 Due Friday January 23, 2009 The starred exercises require the use of Matlab. Remember that it
Math 171A Homework 2 Solutions
Instructor: Jiawang Nie February 1, 2012
1. (8 points) Consider the feasible set F defined by the following constraints x1 + x2 4, x1 + 3x2 6, 6x1 - x2 18, 3 x2 6, x1 -1
Math 171A Homework 3 Solutions
Instructor: Jiawang Nie February 1, 2012
1. (4 points) For a given nonzero matrix A and nonzero vector b, assume that b may be written as b = bR + bN , where bR Range(A)
Math 171A: Linear Programming
Instructor: Philip E. Gill
Winter Quarter 2015
Homework Assignment #3
Due Friday January 30, 2015
Remember that the first midterm exam will be held in class on Wednesday,
Math 171A: Linear Programming
Instructor: Philip E. Gill
Winter Quarter 2015
Homework Assignment #1
Due Friday January 16, 2015
I know that you are all aware of the importance of doing the homework as
Math 140A, Fall 2010, Midterm, 11/8/10
Instructions. Answer all questions. You may use without proof anything which was proved in class. Cite a theorem either by name, if it has one, or by briefly sta
Math 171A: Linear Programming
Instructor: Philip E. Gill
Winter Quarter 2015
Homework Assignment #2
Due Friday January 23rd, 2015
The starred exercises require the use of Matlab. Remember that it is n
Math 171A: Linear Programming
Instructor: Philip E. Gill
Winter Quarter 2017
Homework Assignment #1
Due Wednesday January 25, 2017
I know that you are all aware of the importance of doing the homework
Math 171A: Mathematical Programming
Instructor: Philip E. Gill
Winter Quarter 2009
Homework Assignment #1 Due Friday January 16, 2009 I know that you are all aware of the importance of doing the homew
Math 171A Homework Assignment # 2
Due Date: January 23, 2014
1. (10 points) Consider the linear system Ax = b where
4
3
3
6
2 3
3
6
6
0 ,
A= 1
b= 1
2
1
0
1
6
3
0
5
.
Determine the rank of A and
Math 171A Practice Midterm II
Instructor: Jiawang Nie March 5, 2012
1. Consider the LP of minimizing c 2 3 A = 4 2 3
x subject to Ax b where -15 3 5 -13 4 3 , b = -20 , c = A 5 1 -12 4 4 -13 5 2
0 1
Math 171A: Linear Programming
Instructor: Philip E. Gill
Winter Quarter 2015
Homework Assignment #3
Due Friday January 30, 2015
Remember that the first midterm exam will be held in class on Wednesday,
Math 171A Homework Assignment # 3
Due Date: January 29, 2016
1. (10 points) Let F = cfw_x R2 : 1 x1 x2 1, x2 0. Describe
the sets of vectors c such that:
(a) cT x is bounded from below but unbounded f
Math 171A: Mathematical Programming
Instructor: Philip E. Gill
Winter Quarter 2009
Homework Assignment #2 Due Friday January 23, 2009 The starred exercises require the use of Matlab. Remember that it
Math 171A Homework Assignment # 3
Due Date: January 29, 2016
1. (10 points) Let F = cfw_x R2 : 1 x1 x2 1, x2 0. Describe
the sets of vectors c such that:
(a) cT x is bounded from below but unbounded f
Math 171A: Linear Programming
Instructor: Philip E. Gill
Winter Quarter 2015
Homework Assignment #2
Due Friday January 23rd, 2015
The starred exercises require the use of Matlab. Remember that it is n
Math 171A: Linear Programming
Instructor: Philip E. Gill
Winter Quarter 2015
Homework Assignment #1
Due Friday January 16, 2015
I know that you are all aware of the importance of doing the homework as
Solution of Linear Programming Problems with Matlab
Notation
The transposition operation is denoted by a superscript T (apostrophe in Matlab),
1
T
[1, 2, 3] = 2 ,
3
T
1
2 = [1, 2, 3],
3
1 2 3
4 5 6
Math 171A: Linear Programming
Instructor: Philip E. Gill
Winter Quarter 2015
Homework Assignment #4
Due Friday February 6, 2015
Starred exercises require the use of Matlab.
Exercise 4.1. Suppose that
Math 171A LINEAR PROGRAMMING Class Notes
c 1998. Philip E. Gill, Walter Murray and Margaret H. Wright Department of Mathematics University of California, San Diego, La Jolla, CA 92093-0112. January 20
Recap
Math 171A: Linear Programming
Lecture 2
Properties of Linear Constraints
The lecture slides and homework are posted on the class web-page.
http:/ccom.ucsd.edu/~peg/math171a
Access to course mate
Overview of Math 171A
Math 171A: Linear Programming
Lecture 1
Overview of the Class:
Introduction to Optimization
Philip E. Gill
c 2017
http:/ccom.ucsd.edu/~peg/math171a
TAs: Yesheng Huang (AP&M 5412)
Recap: The graphical method
Math 171A: Linear Programming
1. Graph the feasible region
Lecture 5
Two Methods for Toy Linear Programs
2. Find a corner point of F and a level curve cfw_x : c Tx = z0 su
Recap: Properties of linear constraints
Math 171A: Linear Programming
constraint #1:
constraint #2:
Lecture 4
constraint #3:
Properties of the Objective Function
Philip E. Gill
constraint #4:
constrai
Math 171A: Linear Programming
Lecture 3
Geometry of the Feasible Region
Philip E. Gill
For the Matlab homework, please use the Matlab diary feature.
>
>
>
>
>
diary mysession.txt
.
.
.
diary off
c 201
Recap: column rank
Math 171A: Linear Programming
Lecture 6
What is the smallest number of linearly independent columns of A
(say r ) that completely define range(A)?
Gather r independent columns so th
Math 171A: Linear Programming
So far, we have focused on compatible equations Ax = b.
i.e., equations Ax = b with b range(A).
Lecture 7
Properties of Incompatible Equations
Philip E. Gill
Question
Giv
Math 171A Homework Assignment #3
Due Date: February 2, 2018
1. (10 points) Let F = cfw_x R2 : 1 x1 x2 1, x2 0. Describe
the sets of vectors c such that:
(a) cT x is bounded from below but unbounded fr
Math 171A Homework Assignment #3
Due Date: February 2, 2018
1. (10 points) Let F = cfw_x R2 : 1 x1 x2 1, x2 0. Describe
the sets of vectors c such that:
(a) cT x is bounded from below but unbounded fr
Math 171A Homework Assignment # 4
Due Date: February 16, 2018
1. (10 points) Consider the feasible set F defined by the following constraints
x1 + x2 4,
x1 + 3x2 6,
6x1 x2 18,
3 x2 6,
x1 1.
(a) Expres
Math 171A Homework Assignment #2
Due Date: January 26, 2016
1. (10 points) Consider the linear system Ax = b where
4
3
3
6
2 3
6
3
,
1
1
6
0
A=
b
=
2
1
0
1
6
3
0
5
.
Determine the rank of A and