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Martínez, J. and Qi, L. (1995) Inexact Newton Methods for Solving Nonsmooth Equations. Journal of Computational and Applied Mathematics, 60, 127-145.

has been cited by the following article:

• TITLE: Proximal Methods for Elliptic Optimal Control Problems with Sparsity Cost Functional

  AUTHORS: Andreas Schindele, Alfio Borzì

  KEYWORDS: Optimal Control, Elliptic PDE, Nonsmooth Optimization, Proximal Method, Semismooth Newton Method

  JOURNAL NAME: Applied Mathematics, Vol.7 No.9, May 30, 2016

  ABSTRACT: First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes applied to infinite-dimensional elliptic optimal control problems and to validate the theoretical estimates.