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A solution approach for cardinality minimization problem based on fractional programming

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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,\(card(x)\), 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.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Polytechnic Tehran), Tehran, Iran

    S. M. Mirhadi & S. A. MirHassani

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  1. S. M. Mirhadi
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  2. S. A. MirHassani
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Correspondence to S. A. MirHassani.

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Mirhadi, S.M., MirHassani, S.A. A solution approach for cardinality minimization problem based on fractional programming. J Comb Optim 44, 583–602 (2022). https://doi.org/10.1007/s10878-022-00847-0

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