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International Conference on Relational and Algebraic Methods in Computer Science

RAMICS 2014: Relational and Algebraic Methods in Computer Science pp 362–378Cite as

Complete Solution of a Constrained Tropical Optimization Problem with Application to Location Analysis

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8428))

Abstract

We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective function defined on vectors over an idempotent semifield by means of a conjugate transposition operator, subject to constraints in the form of linear vector inequalities. A complete direct solution to the problem under fairly general assumptions is given in a compact vector form suitable for both further analysis and practical implementation. We apply the result to solve a multidimensional minimax single facility location problem with Chebyshev distance and with inequality constraints imposed on the feasible location area.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Mechanics, Saint Petersburg State University, Universitetsky Ave. 28, 198504, Saint Petersburg, Russia

    Nikolai Krivulin

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  1. Nikolai Krivulin
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Editor information

Editors and Affiliations

  1. NICTA and UNSW, Anzac Parade 223, 2033, Kensington, NSW, Australia

    Peter Höfner

  2. School of Computational Sciences, Chapman University, One University Drive, 92866, Orange, CA, USA

    Peter Jipsen

  3. Department of Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Wolfram Kahl

  4. Department of Computer Science, University of Augsburg, Universitätsstraße 6a, 86159, Augsburg, Germany

    Martin Eric Müller

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Krivulin, N. (2014). Complete Solution of a Constrained Tropical Optimization Problem with Application to Location Analysis. In: Höfner, P., Jipsen, P., Kahl, W., Müller, M.E. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2014. Lecture Notes in Computer Science, vol 8428. Springer, Cham. https://doi.org/10.1007/978-3-319-06251-8_22

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  • DOI: https://doi.org/10.1007/978-3-319-06251-8_22

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06250-1

  • Online ISBN: 978-3-319-06251-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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