title: Second-Order Minimization Method for Nonsmooth Functions Allowing Convex Quadratic Approximations of the Augment
metadata.name: dc.contributor.author
metadata.value: Abbasov, Majid Elkhan ogli
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-04-10T20:47:04Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-04-10T20:47:04Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2015
metadata.lang: -
metadata.name: dc.identifier.issn
metadata.value: 0022-3239
metadata.lang: -
metadata.name: dc.identifier.other
metadata.value: DOI 10.1007/s10957-015-0796-7
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/2042
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Second-order methods play an important role in the theory of optimization. Due to the usage of more information about considered function, they give an opportunity to find the stationary point faster than first-order methods. Well-known and sufficiently studied Newton’s method is widely used to optimize smooth functions. The aim of this work is to obtain a second-order method for unconstrained minimization of nonsmooth functions allowing convex quadratic approximation of the augment. This method is based on the notion of coexhausters—new objects in nonsmooth analysis, introduced by V. F. Demyanov. First, we describe and prove the second-order necessary condition for a minimum. Then, we build an algorithm based on that condition and prove its convergence. At the end of the paper, a numerical example illustrating implementation of the algorithm is given.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: Journal of Optimization Theory and Applications
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: Springer US
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Second-Order Minimization Method for Nonsmooth Functions Allowing Convex Quadratic Approximations of the Augment
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: art%3A10.1007%2Fs10957-015-0796-7.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/2042/1/art%253A10.1007%252Fs10957-015-0796-7.pdf
resources.format: Adobe PDF
resources.description: Second-Order Minimization Method for Nonsmooth Functions Allowing Convex Quadratic Approximations of the Augment
resources.size: 414,26 kB