Convergence of quasi-Newton matrices generated by the symmetric rank one update
Mathematical Programming: Series A and B
Sizing and least-change secant methods
SIAM Journal on Numerical Analysis
CUTE: constrained and unconstrained testing environment
ACM Transactions on Mathematical Software (TOMS)
Local Convergence of the Symmetric Rank-One Iteration
Computational Optimization and Applications
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
A restarting approach for the symmetric rank one update for unconstrained optimization
Computational Optimization and Applications
Improved Hessian approximation with modified secant equations for symmetric rank-one method
Journal of Computational and Applied Mathematics
Structured symmetric rank-one method for unconstrained optimization
International Journal of Computer Mathematics
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Quasi-Newton (QN) methods are generally held to be the most efficient minimization methods for solving unconstrained optimization problems. Among the QN methods, symmetric rank-one (SR1) is one of the very competitive formulas. In the present paper, we propose a new SR1 method. The new technique attempts to improve the quality of the SR1 Hessian by employing the scaling of the identity in a certain sense. However, since at some iterations these updates might be singular, indefinite or undefined, this paper proposes an updates criterion based on the eigenvalues of the SR1 update to measure this quality. Hence, the new method is employed only to improve the approximation of the SR1 Hessian. It is shown that the numerical results support the theoretical considerations for the usefulness of this criterion and show that the proposed method improves the performance of the SR1 update substantially.