Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Unconstrained optimization

Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_1083
  • 27 Downloads

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 from the fields of engineering and science. 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
This is a preview of subscription content, log in to check access.

References

  1. [1]
    Dennis, J.E. and Schnabel, R.B. (1983). Numerical Methods for Unconstrained Optimization and Non-linear Equations, Prentice Hall, Englewood Cliffs, New Jersey.Google Scholar
  2. [2]
    Gill, P.E., Murray, W., and Wright, M.H. (1981). Practical Optimization, Academic Press, New York.Google Scholar
  3. [3]
    Lemarechal, C. (1989). “Nondifferentiable Optimization,” in Optimization, G.L. Nemhauser, A.H.G. Rinnooy Kan, and M. J. Todd, eds., Elsevier, Amsterdam, 529–572.Google Scholar
  4. [4]
    Moré, J.J. and Wright, S.J. (1993). Optimization Soft-ware Guide, SIAM, Philadelphia.Google Scholar
  5. [5]
    Nash, S.G. and Sofer, A. (1996). Linear and Nonlinear Programming, McGraw-Hill, New York.Google Scholar
  6. [6]
    Rinnooy Kan, A.H. G. and Timmer, G.T. (1989). “Global Optimization,” in Optimization, G.L. Nemhauser, A.H.G. Rinnooy Kan, and M. J. Todd, eds., Elsevier, Amsterdam, 631–662.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.George Mason UniversityFairfaxUSA