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Investigation on Perturbed Spectral-Scaling BFGS Method with Nonmonotone Line Search and Its Convergence

Guoping Li


In this paper, A problem on nonconvex function minimization is invested. On the basis of the advantage of the nonmonotone line search and spectral scaling techniques, we develop a perturbed Spectral-Scaling BFGS Method with nonmonotone line search and give a prove on global convergence for it. The different from the exsisting method is that a spectral-scaling and a perturbed factor is introduced into update formula of SSBFGS method. The spectral-scaling factor can decline the condition number of quasi-Newton matrix for large scale problems and The perturbed factor guarantees that this method is grobally convergent for nonconvex minmization problem . At last, we do some numerical experiments to test the proposed methods. The results show that under the same condition, when used to solve large scale problems, the Perturbed SSBFGS method outperforms the SSBFGS.


nonconvex function minimization, nonmonotone line search, pectral scaling technique, global convergence.

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