a BFGS updat‎e FOR UNCONSTRAINED OPTIMIZATION

In this paper, we propose the -BFGS update. We show that under certain circumstances this - BFGS update preserve the value of the determinant of Hessian matrix (second derivative of the objective function). This property guarantees the non-singularity (does not near zero) of the Hessian matrix for a high dimensional problems. Our numerical results support this claim and also indicate that the -BFGS update may be competitive with the BFGS update in general.