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A solution approach for cardinality minimization problem based on fractional programming

Author

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  • S. M. Mirhadi

    (Amirkabir University of Technology (Polytechnic Tehran))

  • S. A. MirHassani

    (Amirkabir University of Technology (Polytechnic Tehran))

Abstract

This paper proposes a new algorithm for solving the linear Cardinality Minimization Problem (CMP). The algorithm relies on approximating the nonconvex and non-smooth function, $$card(x)$$ c a r d ( x ) , with a linear fractional one. Therefore, the cardinality minimization problem is converted to the sum-of-ratio problem. The new model is solved with an optimization algorithm proposed for finding the optimal solution to the ratio problem. In the numerical experiments, we focus on two types of CMP problems with inequality and equality constraints. We provide a series of examples to evaluate the performance of the proposed algorithm, showing its efficiency.

Suggested Citation

  • S. M. Mirhadi & S. A. MirHassani, 2022. "A solution approach for cardinality minimization problem based on fractional programming," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 583-602, August.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:1:d:10.1007_s10878-022-00847-0
    DOI: 10.1007/s10878-022-00847-0
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    References listed on IDEAS

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    1. Jiao, Hong-Wei & Liu, San-Yang, 2015. "A practicable branch and bound algorithm for sum of linear ratios problem," European Journal of Operational Research, Elsevier, vol. 243(3), pages 723-730.
    2. Xiaojun Chen & Weijun Zhou, 2014. "Convergence of the reweighted ℓ 1 minimization algorithm for ℓ 2 –ℓ p minimization," Computational Optimization and Applications, Springer, vol. 59(1), pages 47-61, October.
    3. Shen, Peiping & Zhu, Zeyi & Chen, Xiao, 2019. "A practicable contraction approach for the sum of the generalized polynomial ratios problem," European Journal of Operational Research, Elsevier, vol. 278(1), pages 36-48.
    4. YongJin Kim & YunChol Jong & JinWon Yu, 2021. "A parametric solution method for a generalized fractional programming problem," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(4), pages 971-989, December.
    5. Amir Beck & Yakov Vaisbourd, 2016. "The Sparse Principal Component Analysis Problem: Optimality Conditions and Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 119-143, July.
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