Gauss–Newton-based BFGS method with filter for unconstrained minimization

One class of the lately developed methods for solving optimization problems are filter methods. In this paper we attached a multidimensional filter to the Gauss–Newton-based BFGS method given by Li and Fukushima [D. Li, M. Fukushima, A globally and superlinearly convergent Gauss–Newton-based BFGS method for symmetric nonlinear equations, SIAM Journal of Numerical Analysis 37(1) (1999) 152–172] in order to reduce the number of backtracking steps. The proposed filter method for unconstrained minimization problems converges globally under the standard assumptions. It can also be successfully used in solving systems of symmetric nonlinear equations. Numerical results show reasonably good performance of the proposed algorithm.