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An inexact proximal point method for solving generalized fractional programs

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Abstract

In this paper, we present several new implementable methods for solving a generalized fractional program with convex data. They are Dinkelbach-type methods where a prox-regularization term is added to avoid the numerical difficulties arising when the solution of the problem is not unique. In these methods, at each iteration a regularized parametric problem is solved inexactly to obtain an approximation of the optimal value of the problem. Since the parametric problem is nonsmooth and convex, we propose to solve it by using a classical bundle method where the parameter is updated after each ‘serious step’. We mainly study two kinds of such steps, and we prove the convergence and the rate of convergence of each of the corresponding methods. Finally, we present some numerical experience to illustrate the behavior of the proposed algorithms, and we discuss the practical efficiency of each one.

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Authors and Affiliations

  1. Department of Mathematics, University of Namur (FUNDP), Namur, Belgium

    Jean-Jacques Strodiot & Van Hien Nguyen

  2. LIMOS, CNRS-UMR 6158, Université Blaise Pascal, Clermont-Ferrand, France

    Jean-Pierre Crouzeix

  3. DIRO, Université de Montréal, Montreal, QC, Canada

    Jacques A. Ferland

Authors
  1. Jean-Jacques Strodiot
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  2. Jean-Pierre Crouzeix
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  3. Jacques A. Ferland
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  4. Van Hien Nguyen
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Correspondence to Jean-Jacques Strodiot.

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Strodiot, JJ., Crouzeix, JP., Ferland, J.A. et al. An inexact proximal point method for solving generalized fractional programs. J Glob Optim 42, 121–138 (2008). https://doi.org/10.1007/s10898-007-9270-x

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  • DOI: https://doi.org/10.1007/s10898-007-9270-x

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