Nonsmooth Steepest Descent Method by Proximal Subdifferentials in Hilbert Spaces

Zhou Wei () and Qing Hai He ()
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Zhou Wei: Yunnan University
Qing Hai He: Yunnan University

Journal of Optimization Theory and Applications, 2014, vol. 161, issue 2, No 7, 465-477

Abstract: Abstract In this paper, we first study a nonsmooth steepest descent method for nonsmooth functions defined on a Hilbert space and establish the corresponding algorithm by proximal subgradients. Then, we use this algorithm to find stationary points for those functions satisfying prox-regularity and Lipschitz continuity. As an application, the established algorithm is used to search for the minimizer of a lower semicontinuous and convex function on a finite-dimensional space. A convergence theorem, as an extension and improvement of the existing converging result for twice continuously differentiable convex functions, is also presented therein.

Keywords: Nonsmooth steepest descent method; Stationary point; Proximal subdifferential; Prox-regularity (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0444-z

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