Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2002-004 (February 27, 2002)

Regularized Newton Methods for Convex Minimization Problems with Singular Solutions
by Dong-Hui Li, Masao Fukushima, Liqun Qi and Nobuo Yamashita

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This paper studies convergence properties of regularized Newton methods for minimizing a convex function whose Hessian matrix may be singular everywhere. We show that if the objective function is LC^2, then the methods possess local quadratic convergence under a local error bound condition without the requirement of isolated nonsingular solutions. By using a backtracking line search, we globalize an inexact regularized Newton method. We show that the unit stepsize is accepted eventually.