Globally Convergent BFGS Method for Nonsmooth Convex Optimization1

A. I. Rauf and M. Fukushima
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A. I. Rauf: Hamdard University Islamabad, Markaz
M. Fukushima: Kyoto University

Journal of Optimization Theory and Applications, 2000, vol. 104, issue 3, No 3, 539-558

Abstract: Abstract We propose an implementable BFGS method for solving a nonsmooth convex optimization problem by converting the original objective function into a once continuously differentiable function by way of the 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 the global convergence of the proposed method under the assumption of strong convexity of the objective function.

Keywords: nonsmooth convex optimization; Moreau–Yosida regularization; strong convexity; inexact function and gradient evaluations; BFGS method (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1004633524446

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