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Range division and compression algorithm for quadratically constrained sum of quadratic ratios

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Abstract

In this paper, we present a range division and compression algorithm for effectively solving quadratically constrained sum of quadratic ratios problem. In this algorithm, a novel linear relaxation approach is proposed for deriving linear relaxation programming, which is used to obtain a lower bound of the optimal value of this problem. By utilizing the known upper bound and the constructed linear relaxation programming, a range compression technique is presented to contract the investigated range. Thus, a range division and compression algorithm is constructed and its convergence is proved. Compared with the current approaches, the proposed algorithm does not need to introduce new variables and constraints and it does not need to employ additional procedure to calculate the intervals of numerator and denominator of each ratio, so that this will facilitate the implementation of this algorithm. Finally, numerical comparisons with the known algorithms demonstrate the advantage of the proposed algorithm.

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Acknowledgments

The authors are very grateful to the responsible editor and the anonymous referees for their valuable comments and suggestions, which have greatly improved the earlier version of this article. This paper is supported by the National Natural Science Foundation of China (61373174), the Science and Technology Key Project of Education Department of Henan Province (14A110024), and the Fundamental Research Funds for the Central Universities (JB142001-4).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710126, China

    Hongwei Jiao & Sanyang Liu

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  1. Hongwei Jiao
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  2. Sanyang Liu
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Correspondence to Sanyang Liu.

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Communicated by Natasa Krejic.

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Jiao, H., Liu, S. Range division and compression algorithm for quadratically constrained sum of quadratic ratios. Comp. Appl. Math. 36, 225–247 (2017). https://doi.org/10.1007/s40314-015-0224-5

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  • DOI: https://doi.org/10.1007/s40314-015-0224-5

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