Separating two polyhedra utilizing alternative theorems and penalty function

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>

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's method to solve the unconstrained objective optimization. The computational outcomes demonstrate the efficacy of the proposed method.
Czech name
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Czech description
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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)

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)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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
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