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Robust linear optimization under matrix completion

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Abstract

Linear programming models have been widely used in input-output analysis for analyzing the interdependence of industries in economics and in environmental science. In these applications, some of the entries of the coefficient matrix cannot be measured physically or there exists sampling errors. However, the coefficient matrix can often be low-rank. We characterize the robust counterpart of these types of linear programming problems with uncertainty set described by the nuclear norm. Simulations for the input-output analysis show that the new paradigm can be helpful.

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Authors and Affiliations

  1. School of Management, Shenzhen Polytechnic, Shenzhen, 518055, China

    ShouWen Wen

  2. Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, China

    FangFang Xu & ZaiWen Wen

  3. Institute of Natural Sciences and MOE-LSC, Shanghai Jiaotong University, Shanghai, 200240, China

    ZaiWen Wen

  4. The Center for Economic Research, Shandong University, Jinan, 250100, China

    Chen Lin

Authors
  1. ShouWen Wen
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  2. FangFang Xu
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  3. ZaiWen Wen
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  4. Chen Lin
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Correspondence to ZaiWen Wen.

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Wen, S., Xu, F., Wen, Z. et al. Robust linear optimization under matrix completion. Sci. China Math. 57, 699–710 (2014). https://doi.org/10.1007/s11425-013-4697-7

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