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A reduced subgradient algorithm

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Nonlinear Analysis and Optimization

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

Abstract

In this paper, we propose an iterative algorithm designed to minimize a convex function subject to linear equality and bound constraints. The algorithm generalizes the reduced gradient algorithm of Wolfe while avoiding the hypothesis of differentiability. The set of variables is decomposed into basic and non-basic variables and in order to obtain a method with the descent property of the objective function, the subdifferential is approximated by a bundle which contains a finite number of elements. Each of these vectors is reduced and the search direction for the non-basic variables is obtained by solving an appropriate quadratic problem. Then a descent direction is built in the whole space and an inexact line-search is performed along this one. We discuss the problem of the basis change and we prove the convergence of our algorithm under a very weak condition on the basis choice due to Huard. Finally we give some numerical results of using the algorithm on a number of test problems taken from the literature.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Facultés Universitaires de Namur, Rempart de la Vierge 8, B-5000, Namur, Belgium

    A. Bihain, V. Hien Nguyen & J.-J. Strodiot

Authors
  1. A. Bihain
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  2. V. Hien Nguyen
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  3. J.-J. Strodiot
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Editor information

B. Cornet V. H. Nguyen J. P. Vial

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© 1987 The Mathematical Programming Society, Inc.

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Bihain, A., Nguyen, V.H., Strodiot, JJ. (1987). A reduced subgradient algorithm. 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/BFb0121158

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  • DOI: https://doi.org/10.1007/BFb0121158

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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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