In this paper, we propose a new dwindling multidimensional filter second-order line search method for solving large-scale unconstrained optimization problems. Usually, the multidimensional filter is constructed with a fixed envelope, which is a strict condition for the gradient vectors. A dwindling multidimensional filter technique, which is a modification and improvement of the original multidimensional filter, is presented. Under some reasonable assumptions, the new algorithm is globally convergent to a second-order critical point, when negative curvature direction is exploited. Preliminary numerical experiments on a set of \texttt{CUTEr} test problems indicate that the new algorithm is more competitive than the traditional second-order line search algorithms.
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Technical Report of Optimization No: 2010-09-01, School of Mathematical Science, Nanjing Normal University, Nanjing, China.
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