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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®
Quadratic Programming 269
f(x
) f(x
+ λ
(y x
)),
then since f(x) is a convex function over S, we have
f(x
) f(x
+ λ
(y x
)) = f(λ
y + (1 λ
)x
)
λ
f(y) + (1 λ
)f(x
),
then
f(x
) λ
f(y) + (1 λ
)f(x
),
or equivalently
f(x
) f(y).
Therefore x
is a global minimum. If f(x) is a strictly convex function,
then the inequalities above hold strictly for all y 6= x
.
7.5.4 Equality-Constrained Quadratic Programs
Next we consider equality-constrained quadratic programs (EQP) of the form
minimize f(x) =
1
2
x
T
Qx + c
T
x
subject to Ax = b.
The key idea is to turn an EQP into an unconstrained problem by defining
a new function called the Lagrangian. This is accomplished ...
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Publisher Resources

ISBN: 9781439862636