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Some remarks on the construction of higher order algorithms in convex optimization

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Abstract

Consider the problem of minimizing a real functionalf. A Newton-like method requires first an approximationD(d) off(x + d)−f(x) at the current iteratex, valid for smalld to an order higher than 1, and consists in minimizingD. In this paper, we will introduce a new concept of such an approximation for convex functions without differentiability assumptions. The connections with the classical concept based on the Taylor development of a differentiablef are exhibited. The material is used to study a conceptual (nonimplementable) algorithm. Some hints are given which could lead to an implementable version.

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Authors and Affiliations

  1. INRIA, Le Chesnay, France

    C. Lemaréchal

  2. University of Bayreuth, West Germany

    J. Zowe

Authors
  1. C. Lemaréchal
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  2. J. Zowe
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Communicated by J. Stoer

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Lemaréchal, C., Zowe, J. Some remarks on the construction of higher order algorithms in convex optimization. Appl Math Optim 10, 51–68 (1983). https://doi.org/10.1007/BF01448379

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  • DOI: https://doi.org/10.1007/BF01448379

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