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The optimization problem over a distributive lattice

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Abstract

In this paper we give a necessary and sufficient condition for existence of minimal solution(s) of the linear system A * X ≥ b where A, b are fixed matrices and X is an unknown matrix over a lattice. Next, an algorithm which finds these minimal solutions over a distributive lattice is given. Finally, we find an optimal solution for the optimization problem min {Z = C * X | A * X ≥ b} where C is the given matrix of coefficients of objective function Z.

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Authors and Affiliations

  1. Shiraz Payam-e-Noor University, Shiraz, Iran

    Mahbobeh Hosseinyazdi

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  1. Mahbobeh Hosseinyazdi
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Correspondence to Mahbobeh Hosseinyazdi.

Additional information

This research was completed while the author was a visitor of the Center for Informatics and Applied Optimization, University of Ballarat, Ballarat, Australia.

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Hosseinyazdi, M. The optimization problem over a distributive lattice. J Glob Optim 41, 283–298 (2008). https://doi.org/10.1007/s10898-007-9230-5

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  • DOI: https://doi.org/10.1007/s10898-007-9230-5

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