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Continuous and Convex Extensions Approaches in Combinatorial Optimization

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System Analysis and Artificial Intelligence

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1107))

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Abstract

The paper is dedicated to extensions of functions and applications in combinatorial optimization. We present a review of the main contributions in the area of continuous and smooth extensions of functions, on the basis of which we formulate the singularities of such extensions for finite sets. We consider a class of finite sets coinciding with their convex hull. For such sets, the existence of convex extensions of functions is proved, which makes it possible to apply the methods of convex analysis to solve relaxation problems. For combinatorial sets, we formulated an equivalent statement of the discrete optimization problem with a convex objective function and proposed methods for estimating the optimum.

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Authors and Affiliations

  1. National Aerospace University “Kharkiv Aviation Institute”, 17 Chkalova Street, Kharkiv, 61070, Ukraine

    Sergiy Yakovlev & Oksana Pichugina

  2. Institute of Information Technology, Lodz University of Technology, 116 Zeromskiego Str, 90-924, Lodz, Poland

    Sergiy Yakovlev

  3. Department of Mechanical and Industrial Engineering, University of Toronto, 27 King’s College Cir, Toronto, M5S1A1, Canada

    Oksana Pichugina

Authors
  1. Sergiy Yakovlev
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  2. Oksana Pichugina
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Correspondence to Sergiy Yakovlev .

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Editors and Affiliations

  1. Research Supervisor of the Institute for Applied Systems Analysis, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine

    Michael Zgurovsky

  2. Deputy Director for Research of the Institute for Applied Systems Analysis, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine

    Nataliya Pankratova

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Yakovlev, S., Pichugina, O. (2023). Continuous and Convex Extensions Approaches in Combinatorial Optimization. In: Zgurovsky, M., Pankratova, N. (eds) System Analysis and Artificial Intelligence . Studies in Computational Intelligence, vol 1107. Springer, Cham. https://doi.org/10.1007/978-3-031-37450-0_15

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