by A. I. Rauf, M. Fukushima
Journal of Optimization Theory and Applications
http://halo.kuamp.kyoto-u.ac.jp/zagato/member/staff/fuku/./papers/MY-BFGS-rev.ps.Z
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Abstract:
Abstract. We propose an implementable BFGS method for solving a nonsmooth convex optimization problem by converting the original objective function to a once continuously differentiable function by way of Moreau-Yosida regularization. The proposed method makes use of approximate function and gradient values of the Moreau-Yosida regularization instead of the corresponding exact values. We prove global convergence of the proposed method under the assumption of strong convexity of the objective function. Key Words. Nonsmooth convex optimization, Moreau-Yosida regularization, strong convexity, inexact function and gradient evaluation, BFGS method.
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