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Maximization of a PSD Quadratic Form and Factorization

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00531777" target="_blank" >RIV/67985807:_____/21:00531777 - isvavai.cz</a>

  • Alternative codes found

    RIV/00216208:11320/21:10437016

  • Result on the web

    <a href="http://dx.doi.org/10.1007/s11590-020-01624-w" target="_blank" >http://dx.doi.org/10.1007/s11590-020-01624-w</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/s11590-020-01624-w" target="_blank" >10.1007/s11590-020-01624-w</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Maximization of a PSD Quadratic Form and Factorization

  • Original language description

    We consider the problem of maximization of a convex quadratic form on a convex polyhedral set, which is known to be NP-hard. In particular, we focus on upper bounds on the maximum value. We investigate utilization of different vector norms (estimating the Euclidean one) and different objective matrix factorizations. We arrive at some kind of duality with positive duality gap in general, but with possibly tight bounds. We discuss theoretical properties of these bounds and also extensions to generally preconditioned factors. We employ mainly the maximum vector norm since it yields efficiently computable bounds, however, we study other norms, too. Eventually, we leave many challenging open problems that arose during the research.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • 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

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2021

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Optimization Letters

  • ISSN

    1862-4472

  • e-ISSN

    1862-4480

  • Volume of the periodical

    15

  • Issue of the periodical within the volume

    7

  • Country of publishing house

    DE - GERMANY

  • Number of pages

    14

  • Pages from-to

    2515-2528

  • UT code for WoS article

    000555354000001

  • EID of the result in the Scopus database

    2-s2.0-85088993896