Yazar "Güvenc, İlknur Atasever" için 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 ... -
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 ... -
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. ... -
Vectorization of set-valued maps with respect to total ordering cones and its applications to set-valued optimization problems
Küçük, Mahide; Soyertem, Mustafa; Küçük, Yalçın; Güvenc, İlknur Atasever (Academic Press Inc Elsevier Science, 2012)As a result of our previous studies on finding the minimal element of a set in n-dimensional Euclidean space with respect to a total ordering cone, we introduced a method which we call "The Successive Weighted Sum Method" ... -
Weak Conjugate Duality for Nonconvex Vector Optimization
Küçük, Yalgin; Güvenc, İlknur Atasever; Küçük, Mahide (Yokohama Publishers, 2017)In this work, weak conjugate map, weak biconjugate map and weak subdifferential of a set-valued map are defined by using notions of supremum/infimum of a set and vectorial norm, and relationships among these notions are ... -
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. ...
