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Numerical methods for nondifferentiable convex optimization

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Book cover Nonlinear Analysis and Optimization

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 30))

Abstract

In this paper, we study in Section 1 the proximal method, within a nonexact form for nonsmooth programming. In Section 2 we give a new algorithm, related with the cutting plane method for minimizing on ℝN a convex function that is a sum of a Legendre convex differentiable function and a nondifferentiable convex function. This algorithm is then used in Sections III and IV to solve nonsmooth convex optimization problems in the unconstrained and the constrained cases.

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Authors and Affiliations

  1. Départment de Mathématiques Appliquées, Complexe Scientifique des Cézeaux, Université de Clermont-Ferrand II, B.P. 45, 63170, Aubière, France

    Alfred Auslender

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  1. Alfred Auslender
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B. Cornet V. H. Nguyen J. P. Vial

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© 1987 The Mathematical Programming Society, Inc.

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Auslender, A. (1987). Numerical methods for nondifferentiable convex optimization. In: Cornet, B., Nguyen, V.H., Vial, J.P. (eds) Nonlinear Analysis and Optimization. Mathematical Programming Studies, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121157

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  • DOI: https://doi.org/10.1007/BFb0121157

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00930-3

  • Online ISBN: 978-3-642-00931-0

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