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Convergence of some algorithms for convex minimization

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Abstract

We present a simple and unified technique to establish convergence of various minimization methods. These contain the (conceptual) proximal point method, as well as implementable forms such as bundle algorithms, including the classical subgradient relaxation algorithm with divergent series.

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Authors and Affiliations

  1. Departamento de Matematicas, Universidad de Chile, Santiago, Chile

    Rafael Correa

  2. Domaine de Voluceau-Rocquencourt, INRIA, B.P. 105, 78153, Le Chesnay Cedex, France

    Claude Lemaréchal

Authors
  1. Rafael Correa
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  2. Claude Lemaréchal
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Additional information

An important research work of Phil Wolfe's concerned convex minimization. This paper is dedicated to him, on the occasion of his 65th birthday, in appreciation of his creative and pioneering work.

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Correa, R., Lemaréchal, C. Convergence of some algorithms for convex minimization. Mathematical Programming 62, 261–275 (1993). https://doi.org/10.1007/BF01585170

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  • DOI: https://doi.org/10.1007/BF01585170

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