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

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DOI: 10.1007/BF02592022

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

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## Abstract

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