Yazar "Soyertem, Mustafa" için listeleme
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The generalization of total ordering cones and vectorization to separable Hilbert spaces
Küçük, Mahide; Soyertem, Mustafa; Küçük, Yalçın (Academic Press Inc Elsevier Science, 2012)The characterization of total ordering cones of R-n was given with some properties and optimality conditions in Kucuk et al. (2011) W. In addition, total ordering cones were used to derive a vector valued function from a ... -
Küme değerli dönüşümlerin optimizasyon yöntemleri
Karaman, Emrah (Anadolu Üniversitesi, 2017)Bu çalışmada küme değerli dönüşümlerin optimizasyon yöntemleri incelenmiştir. Kümeleri azaltma (set less) bağıntısına göre verilen küme değerli optimizasyon problemleri için Gerstewitz fonksiyonu kullanılarak vektörizasyon ... -
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 the Scalarization of Set-Valued Optimization Problems with Respect to Total Ordering Cones
Küçük, Mahide; Soyertem, Mustafa; Küçük, Yalçın (Springer-Verlag Berlin, 2011)A construction method of total ordering cone on n dimensional Euclidean space was given, it was shown that any total ordering cone is isomorphic to the lexicographic cone, also, existence of a total ordering cone that ... -
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 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 ... -
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" ... -
Vektör ve küme değerli dönüşümler için yönlü türev ve uygulamaları
Soyertem, Mustafa (Anadolu Üniversitesi, 2012)Bu çalışmada, koniler yardımıyla tanımlanan kısmi sıralamaların tam sıralama tanımlayabilmeleri için bir ek şart verilmiştir. Gerçel ayrılabilir Hilbert uzayının bir dikey tabanı kullanılarak tam sıralama konisi oluşturulması ... -
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. ...
