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On Solving the Quadratic Sum-of-Ratios Problems

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Book cover Mathematical Optimization Theory and Operations Research (MOTOR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12095))

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Abstract

This paper addresses the numerical solution of fractional programs with quadratic functions in the ratios. Instead of considering a sum-of-ratios problem directly, we developed an efficient global search algorithm, which is based on two approaches to the problem. The first one adopts a reduction of the fractional minimization problem to the solution of an equation with an optimal value of a parametric d.c. minimization problem. The second approach reduces the original problem to the optimization problem with nonconvex (d.c.) constraints. Hence, the fractional programs can be solved by applying the Global Search Theory of d.c. optimization.

The global search algorithm developed for sum-of-ratios problems was tested on the examples with quadratic functions in the numerators and denominators of the ratios. The numerical experiments demonstrated that the algorithm performs well when solving rather complicated quadratic sum-of-ratios problems with up to 100 variables or 1000 terms in the sum.

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Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory of SB of RAS, Irkutsk, Russia

    Tatiana V. Gruzdeva & Alexander S. Strekalovsky

Authors
  1. Tatiana V. Gruzdeva
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  2. Alexander S. Strekalovsky
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Correspondence to Tatiana V. Gruzdeva .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Alexander Kononov

  2. Krasovsky Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  3. National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Valery A Kalyagin

  4. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Gruzdeva, T.V., Strekalovsky, A.S. (2020). On Solving the Quadratic Sum-of-Ratios Problems. In: Kononov, A., Khachay, M., Kalyagin, V., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2020. Lecture Notes in Computer Science(), vol 12095. Springer, Cham. https://doi.org/10.1007/978-3-030-49988-4_8

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