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Separating two polyhedra utilizing alternative theorems and penalty function

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10472190" target="_blank" >RIV/00216208:11320/23:10472190 - isvavai.cz</a>

  • Result on the web

    <a href="https://doi.org/10.1007/978-3-031-24866-5_3" target="_blank" >https://doi.org/10.1007/978-3-031-24866-5_3</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/978-3-031-24866-5_3" target="_blank" >10.1007/978-3-031-24866-5_3</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Separating two polyhedra utilizing alternative theorems and penalty function

  • Original language description

    The separation of two polyhedra by a family of parallel hyperplanes is a well-known problem with important applications in operations research,statistics and functional analysis. In this paper, we introduce a new algorithm for constructing a family of parallel hyperplanes that separates two disjoint polyhedra given by a system of linear inequalities. To do this, we consider the alternative system and introduce its dual problem using the alternative theorem. We can find its minimum-norm solution by combining the objective function and constraints into a penalty function. Since our objective function is only once differentiable, we propose an extension of Newton&apos;s method to solve the unconstrained objective optimization. The computational outcomes demonstrate the efficacy of the proposed method.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • OECD FORD branch

    10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Result continuities

  • Project

    <a href="/en/project/GA22-11117S" target="_blank" >GA22-11117S: Global sensitivity analysis and stability in optimization problems</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2023

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Article name in the collection

    Learning and Intelligent Optimization, 16th International Conference, LION 16

  • ISBN

    978-3-031-24866-5

  • ISSN

    0302-9743

  • e-ISSN

  • Number of pages

    13

  • Pages from-to

    27-39

  • Publisher name

    Springer

  • Place of publication

    Berlin

  • Event location

    Milos Island, Greece

  • Event date

    Jun 5, 2022

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article