Maximization of a PSD Quadratic Form and Factorization
Result 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.
Keywords
Convex quadratic formConcave programmingNP-hardnessUpper boundMaximum normPreconditioning
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/00216208:11320/21:10437016
Result on the web
DOI - Digital Object Identifier
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
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Czech description
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Classification
Type
Jimp - 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
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
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Pure mathematics
Year of implementation
2021