Modified Dinkelbach-Type Algorithm for Generalized Fractional Programs with Infinitely Many Ratios

J. Y. Lin and R. L. Sheu
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J. Y. Lin: National Cheng-Kung University
R. L. Sheu: National Cheng-Kung University

Journal of Optimization Theory and Applications, 2005, vol. 126, issue 2, No 6, 323-343

Abstract: Abstract In this paper, we extend the Dinkelbach-type algorithm of Crouzeix, Ferland, and Schaible to solve minmax fractional programs with infinitely many ratios. Parallel to the case with finitely many ratios, the task is to solve a sequence of continuous minmax problems, $$P(\alpha_{k})=\min_{x\in X}\left(\max_{t\in T}\left[f_{t}(x)-\alpha_{k}g_{t}(x) \right]\right)$$ , until {α k } converges to the root of P(α)=0. The solution of P(α k ) is used to generate αk+1. However, calculating the exact optimal solution of P(α k ) requires an extraordinary amount of work. To improve, we apply an entropic regularization method which allows us to solve each problem P(α k ) incompletely, generating an approximate sequence $$\{\tilde{\alpha}_{k}\}$$ , while retaining the linear convergence rate under mild assumptions. We present also numerical test results on the algorithm which indicate that the new algorithm is robust and promising.

Keywords: Generalized fractional programming; minmax problems; entropic regularization (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-005-4717-z

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