A Modified BFGS Algorithm for Unconstrained Optimization

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Abstract
In this paper we present a modified BFGS algorithm for unconstrained optimization. The BFGS algorithm updates an approximate Hessian which satisfies the most recent quasi-Newton equation. The quasi-Newton condition can be interpreted as the interpolation condition that the gradient value of the local quadratic model matches that of the objective function at the previous iterate. Our modified algorithm requires that the function value is matched, instead of the gradient value, at the previous iterate. The modified algorithm preserves the global and local superlinear convergence properties of the BFGS algorithm. Numerical results are presented, which suggest that a slight improvement has been achieved.

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