A characterization of the minimizer of a function

  • D. G. McDowell
Contributed Papers


This paper is intended to give a characterization of the minimum point of a function in terms of the gradient of the function at some other point using some concepts from differential geometry. The function is assumed to have continuous partial derivatives up to and including order four. It is also assumed to have a positive-definite Hessian matrix onR n and a unique minimum point.

Key Words

Optimization unconstrained minimization gradient methods 


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  1. 1.
    Powell, M. J. D.,A Survey of Numerical Methods for Unconstrained Optimization, SIAM Review, Vol. 12, pp. 79–97, 1970.Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • D. G. McDowell
    • 1
  1. 1.Mathematics DepartmentCentral Michigan UniversityMount Pleasant

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