A preconditioning proximal newton method for nondifferentiable convex optimization |
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Authors: | Liqun Qi Xiaojun Chen |
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Institution: | (1) School of Mathematics, University of New South Wales, 2052 Sydney, NSW, Australia |
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Abstract: | We propose a proximal Newton method for solving nondifferentiable convex optimization. This method combines the generalized
Newton method with Rockafellar’s proximal point algorithm. At each step, the proximal point is found approximately and the
regularization matrix is preconditioned to overcome inexactness of this approximation. We show that such a preconditioning
is possible within some accuracy and the second-order differentiability properties of the Moreau-Yosida regularization are
invariant with respect to this preconditioning. Based upon these, superlinear convergence is established under a semismoothness
condition.
This work is supported by the Australian Research Council. |
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Keywords: | Nondifferentiable convex optimization Proximal point Superlinear convergence Newton’ s method |
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