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On Solving the Quadratic Sum-of-Ratios Problems

  • Tatiana V. GruzdevaEmail author
  • Alexander S. Strekalovsky
Conference paper
  • 197 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12095)

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.

Keywords

Fractional optimization Nonconvex problem Difference of two convex functions Quadratic functions Global search algorithm Computational testing 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Matrosov Institute for System Dynamics and Control Theory of SB of RASIrkutskRussia

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