Affine trajectories in a field of strictly convex functions
Result description
The paper presents one important and interesting property of strictly convex functions. On the base of previously proved properties of these functions, we can generalize some global-geometric conclusions, without the even assumption of their differentiability, and also point out some geometric characteristics of the sets of all solutions of parametric optimization problems. Two specific nonlinear parametric optimizations of nonlinear problems - the minimization and the maximization problems - exist forthem. They express a pair of dual optimization problems. The set of all optimal points has an important geometric interpretation. This paper connects the proved properties of a specific case and a geometric sense.
Keywords
Strictly convex functionnonlinear parametric optimization problemaffine trajectory in the field of the strictly convex functionaffine normal at points of the smooth hyperplane
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Affine trajectories in a field of strictly convex functions
Original language description
The paper presents one important and interesting property of strictly convex functions. On the base of previously proved properties of these functions, we can generalize some global-geometric conclusions, without the even assumption of their differentiability, and also point out some geometric characteristics of the sets of all solutions of parametric optimization problems. Two specific nonlinear parametric optimizations of nonlinear problems - the minimization and the maximization problems - exist forthem. They express a pair of dual optimization problems. The set of all optimal points has an important geometric interpretation. This paper connects the proved properties of a specific case and a geometric sense.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
AIP proceedings
ISSN
0094-243X
e-ISSN
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Volume of the periodical
1631/ 2014
Issue of the periodical within the volume
276
Country of publishing house
US - UNITED STATES
Number of pages
6
Pages from-to
276-281
UT code for WoS article
000346058100038
EID of the result in the Scopus database
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Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2015