MthSc 810: Mathematical Programming
Lecture 11
Pietro Belotti
Dept. of Mathematical Sciences
Clemson University
October 6, 2011
Reading for today: Sections 3.7 and 4.1-4.2, textbook
Reading for Oct. 11: Sections 4.3-4.4, textbook
Homework #7 is out! Due October 13, 2011
Midterm 2: November 1, 2011, 2pm
How fast is the simplex method?
Consider an LP in standard form identified by
(
n
,
m
,
c
,
A
,
b
)
.
◮
How much time does it take to solve this problem?
◮
Time is hard to measure (due to computer speed etc.).
◮
However, the sequence of iterations doesn’t change
1
⇒
Better question: in how many
simple
steps
(sums/products/etc.) do we solve an LP?
◮
It could be a function
f
(
n
,
m
,
c
,
A
,
b
)
, still too complicated.
Q.
Given
m
,
n
, what is the
maximum
number of steps to solve
an LP problem with
n
variables and
m
constraints?
T
(
n
,
m
) :=
max
{
f
(
n
,
m
,
c
,
A
,
b
) :
A
∈
Q
m
×
n
,
c
∈
Q
n
,
b
∈
Q
m
}
◮
This is called the
worst-casecomplexity
of an algorithm.
1
Assuming we are given the same instructions.