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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Optimization of Quadratic Forms and t-norm Forms on Interval Domain and Computational Complexity
Original language description
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.
Czech name
—
Czech description
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Project
<a href="/en/project/GA18-04735S" target="_blank" >GA18-04735S: Novel approaches for relaxation and approximation techniques in deterministic global optimization</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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