Kurum Yazarı "Küçük, Yalçın" Fakülteler İçin Listeleme
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Generalized weak subdifferentials
Küçük, Yalçın; Güvenc, İlknur Atasever; Küçük, Mahide (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 ... -
Large margin classifiers based on affine hulls
Çevikalp, Hakan; Triggs, Bill; Yavuz, Hasan Serhan; Küçük, Yalçın; Küçük, Mahide; Barkana, Atalay (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 ... -
Minkowski-Radstrom-Hormander Cone
Grzybowski, Jerzy; Küçük, Mahide; Küçük, Yalçın; Urbanski, Ryszard (Yokohama Publishers, 2014)In this paper we introduce and investigate the notion of the generalized Minkowski-Radstrom Hormander cone giving a special attention to the order law of cancellation. In particular we embed the convex cone e(X) of nonempty ... -
On constructing total orders and solving vector optimization problems with total orders
Küçük, Mahide; Soyertem, Mustafa; Küçük, Yalçın (Springer, 2011)In this paper, we introduce a construction method of total ordering cone on R(n). It is shown that any total ordering cone on Rn is isomorphic to the cone R(lex)(n). Existence of a total ordering cone that contain given ... -
On generalized weak subdifferentials and some properties
Küçük, Yalçın; Güvenc, İlknur Atasever; Küçük, Mahide (Taylor & Francis LTD, 2012)In this article, some characterizations for gw-subdifferentiability of functions from R-n to R-m are stated. Some criteria for gw-subdifferentiability of generalized lower locally Lipschitz functions and positively homogeneous ... -
On minimal representations by a family of sublinear functions
Grzybowski, Jerzy; Küçük, Mahide; Küçük, Yalçın; Urbanski, Ryszard (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 ... -
On solution of boundary value problem for differential inclusion
Küçük, Mahide; Guseinov, Khalik G.; Küçük, Yalçın (Pergamon-Elsevier Science LTD, 2000)In the article an inverse problem for differential inclusion is considered. For a given compact set M-* subset of R-n it is required to define the maximal set M-0 subset of R-n so that the reachable set of differential ... -
On some geometric conditions for minimality of DCH-functions via DC-duality approach
Küçük, Mahide; Tozkan, Didem; Küçük, Yalçın (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 unified theory for continuities
Küçük, Mahide; Küçük, Yalçın (2002)The purpose of this study is to give a unified theory for some weak and strong continuous functions using operations -
Partial order relations on family of sets and scalarizations for set optimization
Karaman, Emrah; Soyertem, Mustafa; Güvenc, İlknur Atasever; Tozkan, Didem; Küçük, Mahide; Küçük, Yalçın (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 ... -
Reduction of Weak Exhausters and Optimality Conditions via Reduced Weak Exhausters
Küçük, Mahide; Urbanski, Ryszard; Grzybowski, Jerzy; Küçük, Yalçın; Güvenc, İlknur Atasever; Tozkan, Didem; Soyertem, Mustafa (Springer/Plenum Publishers, 2015)In this work, it is proved that weak exhausters of a positively homogeneous function can be reduced if weak subdifferential/superdifferential can be represented as the sum of a subset of it and weak subdifferential of zero ... -
Some relationships among gw-subdifferential, directional derivative and radial epiderivative for nonconvex vector functions
Küçük, Yalçın; Güvenc, İlknur Atasever; Küçük, Mahide (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 ... -
Some relationships among quasidifferential, weak subdifferential and exhausters
Küçük, Mahide; Urbanski, Ryszard; Grzybowski, Jerzy; Küçük, Yalçın; Güvenc, İlknur Atasever; Tozkan, Didem; Soyertem, Mustafa (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. ... -
A vectorization for nonconvex set-valued optimization
Karaman, Emrah; Atasever Güvenc, İlknur; Soyertem, Mustafa; Tozkan, Didem; Küçük, Mahide; Küçük, Yalçın (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 Fenchel and weak Fenchel-Lagrange conjugate duality for nonconvex scalar optimization problems
Küçük, Yalçın; Güvenc, İlknur Atasever; Küçük, Mahide (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 ... -
Weak subdifferential/superdifferential, weak exhausters and optimality conditions
Küçük, Mahide; Urbanski, Ryszard; Grzybowski, Jerzy; Küçük, Yalçın; Güvenc, İlknur Atasever; Tozkan, Didem; Soyertem, Mustafa (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. ...