Optimization of Quadratic Forms and t-norm Forms on Interval Domain and Computational Complexity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10437061" target="_blank" >RIV/00216208:11320/21:10437061 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-030-47124-8_9" target="_blank" >https://doi.org/10.1007/978-3-030-47124-8_9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-47124-8_9" target="_blank" >10.1007/978-3-030-47124-8_9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Optimization of Quadratic Forms and t-norm Forms on Interval Domain and Computational Complexity

Popis výsledku v původním jazyce

We consider the problem of maximization of a quadratic form over a box. We identify the NP-hardness boundary for sparse quadratic forms: the problem is polynomially solvable for nonzero entries, but it is NP-hard if the number of nonzero entries is of the order for an arbitrarily small. Then we inspect further polynomially solvable cases. We define a sunflower graph over the quadratic form and study efficiently solvable cases according to the shape of this graph (e.g. the case with small sunflower leaves or the case with a restricted number of negative entries). Finally, we define a generalized quadratic form, called t-norm form, where the quadratic terms are replaced by t-norms. We prove that the optimization problem remains NP-hard with an arbitrary Lipschitz continuous t-norm. (C) 2021, Springer Nature Switzerland AG.

Název v anglickém jazyce

Optimization of Quadratic Forms and t-norm Forms on Interval Domain and Computational Complexity

Popis výsledku anglicky

We consider the problem of maximization of a quadratic form over a box. We identify the NP-hardness boundary for sparse quadratic forms: the problem is polynomially solvable for nonzero entries, but it is NP-hard if the number of nonzero entries is of the order for an arbitrarily small. Then we inspect further polynomially solvable cases. We define a sunflower graph over the quadratic form and study efficiently solvable cases according to the shape of this graph (e.g. the case with small sunflower leaves or the case with a restricted number of negative entries). Finally, we define a generalized quadratic form, called t-norm form, where the quadratic terms are replaced by t-norms. We prove that the optimization problem remains NP-hard with an arbitrary Lipschitz continuous t-norm. (C) 2021, Springer Nature Switzerland AG.

Druh

C - Kapitola v odborné knize

CEP obor

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OECD FORD obor

50201 - Economic Theory

Projekt

<a href="/cs/project/GA18-04735S" target="_blank" >GA18-04735S: Nové přístupy pro relaxační a aproximační techniky v deterministické globální optimalizaci</a><br>

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název knihy nebo sborníku

Studies in Fuzziness and Soft Computing

ISBN

978-3-030-47124-8

Počet stran výsledku

8

Strana od-do

101-108

Počet stran knihy

576

Název nakladatele

Springer

Místo vydání

Cham

Kód UT WoS kapitoly

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