title: Generalized exhausters: Existence, construction, optimality conditions
metadata.name: dc.contributor.author
metadata.value: Abbasov, Majid Elkhan ogli
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-04-10T20:36:30Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-04-10T20:36:30Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2015-01
metadata.lang: -
metadata.name: dc.identifier.other
metadata.value: doi:10.3934/jimo.2015.11.217
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/2041
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this work a generalization of the notion of exhauster is considered. Exhausters are new tools in nonsmooth analysis introduced in works of Demyanov V.F., Rubinov A.M., Pshenichny B.N. In essence, exhausters are families of convex compact sets, allowing to represent the increments of a function at a considered point in an infmax or supmin form, the upper exhausters used for the first representation, and the lower one for the second representation. Using this objects one can get new optimality conditions, find descent and ascent directions and thus construct new optimization algorithms. Rubinov A.M. showed that an arbitrary upper or lower semicontinuous positively homogenous function bounded on the unit ball has an upper or lower exhausters respectively. One of the aims of the work is to obtain the similar result under weaker conditions on the function under study, but for this it is necessary to use generalized exhausters - a family of convex (but not compact!) sets, allowing to represent the increments of the function at a considered point in the form of infsup or supinf. The resulting existence theorem is constructive and gives a theoretical possibility of constructing these families. Also in terms of these objects optimality conditions that generalize the conditions obtained by Demyanov V.F., Abbasov M.E. are stated and proved. As an illustration of obtained results, an example of n-dimensional function, that has a non-strict minimum at the origin, is demonstrated. A generalized upper and lower exhausters for this function at the origin are constructed, the necessary optimality conditions are obtained and discussed.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: Journal of Industrial and Management Optimization (JIMO)
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Generalized exhausters: Existence, construction, optimality conditions
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 9968.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/2041/1/9968.pdf
resources.format: Adobe PDF
resources.description: GENERALIZED EXHAUSTERS: EXISTENCE, CONSTRUCTION, OPTIMALITY CONDITIONS
resources.size: 353,69 kB