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>Regularized Newton methods for convex minimization problems with singular solutions
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Regularized Newton methods for convex minimization problems with singular solutions
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机译:具有奇异解的凸极小化问题的正则牛顿法
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摘要
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 LC2, 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 melhod. We show that the unit stepsize is accepted eventually. Limited numerical experiments are presented, which show the practical advantage of the method.
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