On methods for converting exhausters of positively homogeneous functions. (3rd March 2016)

• Record Type: Journal Article
• Authors: Gorokhovik, Valentin V.; Trafimovich, Marina A.
• Is Part Of: Optimization. Volume 65:Number 3(2016)
• Page Start: 589
• Page End: 608
• Publication Date: 2016-03-03
• Subjects: positively homogeneous function -- exhauster -- convertor; 49J52; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1032285
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In the paper we develop a method for converting a (not necessarily uniformly bounded) upper (lower) primal exhauster of a continuous positively homogeneous function to a lower (upper) primal exhauster of the same function. The method is based on representation of a continuous positively homogeneous function as a pointwise supremum (infimum) of an one-parameter monotone family of Lipschitz continuous positively homogeneous functions that is of independent interest.