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Introduction to Linear Optimization and Extensions with MATLAB®
book

Introduction to Linear Optimization and Extensions with MATLAB®

by Roy H. Kwon
September 2013
Intermediate to advanced content levelIntermediate to advanced
362 pages
8h 44m
English
CRC Press
Content preview from Introduction to Linear Optimization and Extensions with MATLAB®
148 Introduction to Linear Optimization and Extensions with MATLAB
R
Table 4.4 Primal complementary
slackness for Example 4.11
Optimal primal Dual slack Product
x
1
= 0 π
4
= 25 0
x
2
= 5.5 π
5
= 0 0
x
3
= 7 π
6
= 0 0
Table 4.5 Dual complementary
slackness for Example 4.11
Optimal dual Primal slack Product
π
1
= 0 x
4
= 21.5 0
π
2
= 7.5 x
5
= 0 0
π
3
= 30 x
6
= 0 0
4.5.1 Complementary Slackness for Standard Form
Now consider the primal problem P in standard form:
minimize c
T
x
subject to Ax = b
x 0
with its dual D
maximize b
T
π
subject to A
T
π c
π unrestricted.
For this case, note that any feasible solution x of the primal problem P
will satisfy condition (2) of complementary slackness, ...
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Publisher Resources

ISBN: 9781439862636