ISE 536–Fall03: Linear Programming and Extensions
November 19, 2003
Lecture 21: Interior Point Methods
Lecturer: Fernando Ord´
o˜nez
1
Complexity of LP
The Klee-Minty example says:
To measure the efficiency of an algorithm, we need:
•
Size of an instance.
For example, consider the LP:
min
c
t
x
s
.
t
.
Ax
=
b
x
≥
0
Size is:
•
Count number of elementary operations, (use
O
(
·
) notation to simplify the count.)
For example, the number of operations of the simplex method in the Klee-Minty
example is:
What about the number of operations of the simplex method in the Klee-Minty ex-
ample if we start from point (1
, . . . ,
1)?
Two instances of the same size can have different running times!
We need:
Worst Case
running time of algorithm
A
: The maximum running time of
A
for instances of a given size.
1
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For example: The worst running time over all LPs with
n
variables,
m
constraints.
Worst-case complexity of the Simplex Method?
Is there and algorithm that is polynomial for LP?
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- Spring '05
- YY
- Analysis of algorithms, ellipsoid algorithm, min cT, Ellipsoid method
-
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