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Lagrangian decomposition of block-separable mixed-integer all-quadratic programs

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Abstract.

The purpose of this paper is threefold. First we propose splitting schemes for reformulating non-separable problems as block-separable problems. Second we show that the Lagrangian dual of a block-separable mixed-integer all-quadratic program (MIQQP) can be formulated as an eigenvalue optimization problem keeping the block-separable structure. Finally we report numerical results on solving the eigenvalue optimization problem by a proximal bundle algorithm applying Lagrangian decomposition. The results indicate that appropriate block-separable reformulations of MIQQPs could accelerate the running time of dual solution algorithms considerably.

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Authors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, D-12489, Berlin, Germany

    Ivo Nowak

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  1. Ivo Nowak
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Correspondence to Ivo Nowak.

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The work was supported by the German Research Foundation (DFG) under grant NO 421/2-1

Mathematics Subject Classification (2000): 90C22, 90C20, 90C27, 90C26, 90C59

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Nowak, I. Lagrangian decomposition of block-separable mixed-integer all-quadratic programs. Math. Program. 102, 295–312 (2005). https://doi.org/10.1007/s10107-003-0500-9

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