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Minimization of the Ratio of Functions Defined as Sums of the Absolute Values

Author

Listed:
  • H. Konno

    (Chuo University)

  • K. Tsuchiya

    (Chuo University)

  • R. Yamamoto

    (Chuo University
    Mitsubishi UFJ Trust Investment Technology Institute Company)

Abstract

This paper addresses a new class of linearly constrained fractional programming problems where the objective function is defined as the ratio of two functions which are the sums of the absolute values of affine functions. This problem has an important application in financial optimization. This problem is a convex-convex type of fractional program which cannot be solved by standard algorithms. We propose a branch-and-bound algorithm and an integer programming algorithm. We demonstrate that a fairly large scale problem can be solved within a practical amount of time.

Suggested Citation

  • H. Konno & K. Tsuchiya & R. Yamamoto, 2007. "Minimization of the Ratio of Functions Defined as Sums of the Absolute Values," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 399-410, December.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:3:d:10.1007_s10957-007-9284-z
    DOI: 10.1007/s10957-007-9284-z
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    References listed on IDEAS

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    1. Lo, Andrew W. & Mackinlay, A. Craig, 1997. "Maximizing Predictability In The Stock And Bond Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 1(1), pages 102-134, January.
    2. R. Yamamoto & H. Konno, 2007. "An Efficient Algorithm for Solving Convex–Convex Quadratic Fractional Programs," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 241-255, May.
    3. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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    Cited by:

    1. Hiroshi Konno & Yuuhei Morita & Rei Yamamoto, 2010. "A maximal predictability portfolio using absolute deviation reformulation," Computational Management Science, Springer, vol. 7(1), pages 47-60, January.

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