Abstract
A dwindling multidimensional filter is proposed and applied to a second-order line search framework for unconstrained optimization. Usually, the multidimensional filter is built up with a fixed envelope, which is not well-suited to line search frameworks. In this paper, we propose the dwindling multidimensional filter, whose envelope is dwindling as the step-length of line search decreasing. Combining the dwindling multidimensional filter and a second-order line search, the new algorithm globally converges to a second-order critical point, when the negative curvature direction is exploited. Detailed numerical results on small and large CUTE test problems indicate that the new algorithm is more competitive than some classical line search methods.
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