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Published in:
2016 | OriginalPaper | Chapter
7. Basic Properties of Solutions and Algorithms
Authors : David G. Luenberger, Yinyu Ye
Published in: Linear and Nonlinear Programming
Publisher: Springer International Publishing
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Abstract
In this chapter we consider optimization problems of the form where f is a real-valued function and Ω, the feasible set, is a subset of E
n
. Throughout most of the chapter attention is restricted to the case where Ω = E
n
, corresponding to the completely unconstrained case, but sometimes we consider cases where Ω is some particularly simple subset of E
n
.
$$\displaystyle\begin{array}{rcl} & & \mathrm{minimize}\quad f(\mathbf{x}) \\ & & \mathrm{subject\ to}\quad \mathbf{x} \in \mathrm{\varOmega },{}\end{array}$$
(7.1)