Encyclopedia of Operations Research and Management Science

2013 Edition
| Editors: Saul I. Gass, Michael C. Fu

Unconstrained Optimization

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DOI: https://doi.org/10.1007/978-1-4419-1153-7_1083
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Introduction

Unconstrained optimization is concerned with finding the minimizing or maximizing points of a nonlinear function, where the variables are free to take on any value. Unconstrained optimization problems occur in a wide range of applications in science and engineering. A rich source of unconstrained optimization problems are data-fitting problems, in which some model function with unknown parameters is fitted to data, using some criterion of best fit. This criterion may be the minimum sum of squared errors, or the maximum of a likelihood or entropy function. Unconstrained problems also arise from constrained optimization problems, since these are often solved by solving a sequence of unconstrained problems.

In mathematical terms, an unconstrained minimization problem can be written in the form
$$ \mathrm{{\rm minimize}}\ \:f(\boldsymbol x), $$
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References

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Systems Engineering and Operations ResearchGeorge Mason UniversityFairfaxUSA