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Alternating direction method of multipliers as a simple effective heuristic for mixed-integer nonlinear optimization

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Abstract

In this paper we propose to utilize a variation of the alternating direction method of multipliers (ADMM) as a simple heuristic for mixed-integer nonlinear optimization problems in structural optimization. Numerical experiments suggest that using multiple restarts of ADMM with random initial points often yields a reasonable solution with small computational cost.

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Notes

  1. For S not convex, the projection of a point onto S is not necessarily unique.

  2. This projection is not necessarily unique, since a finite set Zj is nonconvex (unless it is a singleton). If there exist two elements closest to \(x_{j}^{k + 1} + {v_{j}^{k}}\), we may adopt either one.

  3. We set the emphasis mip parameter of CPLEX to 4. This option emphasizes to find hidden feasible solutions with high qualities (IBM Knowledge Center 2017). If we use the default setting, CPLEX requires much more time to find the solutions mentioned here.

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Acknowledgments

The work of the first author is partially supported by JSPS KAKENHI 17K06633.

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Authors and Affiliations

  1. Mathematics and Informatics Center, The University of Tokyo, Hongo 7-3-1, Tokyo, 113-8656, Japan

    Yoshihiro Kanno

  2. Faculty of Mechanical Engineering, Institute of Science and Engineering, Kanazawa University, Kakuma-machi, Kanazawa, 920-11992, Japan

    Satoshi Kitayama

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  1. Yoshihiro Kanno
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  2. Satoshi Kitayama
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Correspondence to Yoshihiro Kanno.

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Communicated by: Qing Li

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Kanno, Y., Kitayama, S. Alternating direction method of multipliers as a simple effective heuristic for mixed-integer nonlinear optimization. Struct Multidisc Optim 58, 1291–1295 (2018). https://doi.org/10.1007/s00158-018-1946-y

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