Mathematical Programming

, 36:145

Symmetric minimum-norm updates for use in gibbs free energy calculations

  • Douglas E. Salane

DOI: 10.1007/BF02592022

Cite this article as:
Salane, D.E. Mathematical Programming (1986) 36: 145. doi:10.1007/BF02592022


This paper examines a type of symmetric quasi-Newton update for use in nonlinear optimization algorithms. The updates presented here impose additional properties on the Hessian approximations that do not result if the usual quasi-Newton updating schemes are applied to certain Gibbs free energy minimization problems. The updates derived in this paper are symmetric matrices that satisfy a given matrix equation and are least squares solutions to the secant equation. A general representation for this class of updates is given. The update in this class that has the minimum weighted Frobenius norm is also presented.

Key words

Gibbs free energy Symmetric updates nonlinear optimization 

Copyright information

© The Mathematical Programming Society, Inc. 1986

Authors and Affiliations

  • Douglas E. Salane
    • 1
  1. 1.Sandia National LaboratoriesAlbuquerqueUSA

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