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Toplam kayıt 16, listelenen: 1-10
Partial order relations on family of sets and scalarizations for set optimization
(Springer, 2018)
In this study, some new order relations on family of sets are introduced by using Minkowski difference. The relations between these orders and the ordering cone of the vector space are obtained. It is shown that depending ...
A vectorization for nonconvex set-valued optimization
(Scientific Technical Research Council Turkey-Tubitak, 2018)
Vectorization is a technique that replaces a set-valued optimization problem with a vector optimization problem. In this work, by using an extension of the Gerstewitz function, a vectorizing function is defined to replace ...
Weak subdifferential/superdifferential, weak exhausters and optimality conditions
(Taylor & Francis LTD, 2015)
In this work, the notion of weak superdifferential is presented. Some calculation rules are given to evaluate weak subdifferential and weak superdifferential of some classes of functions represented by support functions. ...
Large margin classifiers based on affine hulls
(Elsevier Science BV, 2010)
This paper introduces a geometrically inspired large margin classifier that can be a better alternative to the support vector machines (SVMs) for the classification problems with limited number of training samples. In ...
Generalized weak subdifferentials
(Taylor & Francis LTD, 2011)
In this article, generalized weak subgradient (gw-subgradient) and generalized weak subdifferential (gw-subdifferential) are defined for nonconvex functions with values in an ordered vector space. Convexity and closedness ...
On some geometric conditions for minimality of DCH-functions via DC-duality approach
(Springer, 2017)
In this study, some optimality conditions for DCH-functions are given in terms of -faces using DC-duality approach. We introduce some geometric characterizations for the solution set of DCH-minimization problems by means ...
On minimal representations by a family of sublinear functions
(Springer, 2015)
This paper is a continuation of Grzybowski et al. (J Glob Optim 46:589-601, 2010) and is motivated by the study of exhausters i.e. families of closed convex sets. By Minkowski duality closed convex sets correspond to ...
Some relationships among gw-subdifferential, directional derivative and radial epiderivative for nonconvex vector functions
(Taylor & Francis LTD, 2015)
In this work, we give some characterizations of gw-subdifferentiability of a vector-valued function by using its directional derivative and radial epiderivative. Moreover, under some assumptions, we proved that the directional ...
Weak Fenchel and weak Fenchel-Lagrange conjugate duality for nonconvex scalar optimization problems
(Springer, 2012)
In this work, by using weak conjugate maps given in (Azimov and Gasimov, in Int J Appl Math 1:171-192, 1999), weak Fenchel conjugate dual problem, , and weak Fenchel Lagrange conjugate dual problem are constructed. Necessary ...
Some relationships among quasidifferential, weak subdifferential and exhausters
(Taylor & Francis LTD, 2016)
In this study, some relationships between quasidifferentiability and weakly subdifferentiability of a function are investigated, and some results on calculating the quasidifferential in terms of weak exhausters are presented. ...