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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®
312 Introduction to Linear Optimization and Extensions with MATLAB
R
minimize 2x
1
+ 3x
2
subject to a
11
x
1
+ a
12
x
2
b
1
a
21
x
1
+ a
22
x
2
b
2
.
If the constraint and the right-hand side coefficients are uncertain, then
the robust counterpart RC is
minimize 2x
1
+ 3x
2
subject to a
11
x
1
+ a
12
x
2
b
1
a
21
x
1
+ a
22
x
2
b
2

a
11
a
12
a
21
a
22

b
1
b
2

U R
2×2
× R
2×1
.
Note: An element of U is the direct product of a 2 × 2 matrix and a 2 ×1
vector, and so two sets of matrix brackets were used to highlight the dimension
of the direct product. From here on such an element will be represented using
only one bracket for ease of exposition, i.e.,
a
11
a
12
a
21
a
22

b
1
b
2
=
a
11
a
12
b
1
a
21
a
22
b
2
and
(a
i
, b
i
) = (a
i1
, a
i2
, b
i
).
If U =

0.95 1.95 0.95
2.95 1.95 1.95
,
1 2 1
3 2 2
,
1.05 2.05 1.05
3.05 2.05
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Publisher Resources

ISBN: 9781439862636