Positively Homogeneous Functions Revisited

Valentin V. Gorokhovik () and Marina Trafimovich ()
Additional contact information
Valentin V. Gorokhovik: National Academy of Sciences of Belarus
Marina Trafimovich: Belorussian State University

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 2, No 9, 503 pages

Abstract: Abstract The paper deals with positively homogeneous functions defined on a finite-dimensional space. Our attention is mainly focused on those subspaces of positively homogeneous functions that are important in nonsmooth analysis and optimization: the subspace of continuous positively homogeneous functions, of Lipschitz continuous positively homogeneous functions, of difference sublinear functions, and of piecewise linear functions. We reproduce some known results and present a number of new ones, in particular, those that concern Lipschitz continuous positively homogeneous functions.

Keywords: Positive homogeneity; Lipschitz continuity; Difference sublinearity; Piecewise linear function; 49J52; 54C35 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-016-0891-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:171:y:2016:i:2:d:10.1007_s10957-016-0891-4

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-016-0891-4

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().