Kasimbeyli̇, Refail
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Kasimbeyli, R.
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34345345@ieu.edu.tr
Main Affiliation
05.09. Industrial Engineering
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Former Staff
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Documents
48
Citations
637
h-index
14
Documents
62
Citations
1165
Scholarly Output
16
Articles
11
Views / Downloads
4/3
Supervised MSc Theses
0
Supervised PhD Theses
0
WoS Citation Count
403
Scopus Citation Count
367
WoS h-index
11
Scopus h-index
11
Patents
0
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0
WoS Citations per Publication
25.19
Scopus Citations per Publication
22.94
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3
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0
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| Journal | Count |
|---|---|
| Optımızatıon | 2 |
| Sıam Journal on Optımızatıon | 2 |
| 24th Mini EURO Conference on Continuous Optimization and Information-Based Technologies in the Financial Sector, MEC EurOPT 2010 | 2 |
| Infor | 1 |
| Journal of Computatıonal And Applıed Mathematıcs | 1 |
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15 results
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Article Citation - WoS: 24Citation - Scopus: 25A Novel Piecewise Linear Classifier Based on Polyhedral Conic and Max-Min Separabilities(Springer, 2013) Bagirov, Adil M.; Ugon, Julien; Webb, Dean; Ozturk, Gurkan; Kasimbeyli̇, RefailIn this paper, an algorithm for finding piecewise linear boundaries between pattern classes is developed. This algorithm consists of two main stages. In the first stage, a polyhedral conic set is used to identify data points which lie inside their classes, and in the second stage we exclude those points to compute a piecewise linear boundary using the remaining data points. Piecewise linear boundaries are computed incrementally starting with one hyperplane. Such an approach allows one to significantly reduce the computational effort in many large data sets. Results of numerical experiments are reported. These results demonstrate that the new algorithm consistently produces a good test set accuracy on most data sets comparing with a number of other mainstream classifiers.Conference Object Citation - WoS: 14Citation - Scopus: 17A Two-Objective Mathematical Model Without Cutting Patterns for One-Dimensional Assortment Problems(Elsevier Science Bv, 2011) Kasimbeyli, Nergiz; Sarac, Tugba; Kasimbeyli̇, RefailThis paper considers a one-dimensional cutting stock and assortment problem. One of the main difficulties in formulating and solving these kinds of problems is the use of the set of cutting patterns as a parameter set in the mathematical model. Since the total number of cutting patterns to be generated may be very huge, both the generation and the use of such a set lead to computational difficulties in solution process. The purpose of this paper is therefore to develop a mathematical model without the use of cutting patterns as model parameters. We propose a new, two-objective linear integer programming model in the form of simultaneous minimization of two contradicting objectives related to the total trim loss amount and the total number of different lengths of stock rolls to be maintained as inventory, in order to fulfill a given set of cutting orders. The model does not require pre-specification of cutting patterns. We suggest a special heuristic algorithm for solving the presented model. The superiority of both the mathematical model and the solution approach is demonstrated on test problems. (C) 2010 Elsevier B.V. All rights reserved.Article Citation - WoS: 47Citation - Scopus: 49A Conic Scalarization Method in Multi-Objective Optimization(Springer, 2013) Kasimbeyli̇, RefailThis paper presents the conic scalarization method for scalarization of nonlinear multi-objective optimization problems. We introduce a special class of monotonically increasing sublinear scalarizing functions and show that the zero sublevel set of every function from this class is a convex closed and pointed cone which contains the negative ordering cone. We introduce the notion of a separable cone and show that two closed cones (one of them is separable) having only the vertex in common can be separated by a zero sublevel set of some function from this class. It is shown that the scalar optimization problem constructed by using these functions, enables to characterize the complete set of efficient and properly efficient solutions of multi-objective problems without convexity and boundedness conditions. By choosing a suitable scalarizing parameter set consisting of a weighting vector, an augmentation parameter, and a reference point, decision maker may guarantee a most preferred efficient or properly efficient solution.Article Citation - WoS: 79A Nonlinear Cone Separation Theorem and Scalarization in Nonconvex Vector Optimization(Siam Publications, 2010) Kasimbeyli̇, RefailIn this paper, a special separation property for two closed cones in Banach spaces is proposed, and a nonlinear separation theorem for the cones possessing this property is proved. By extending a usual definition of dual cones, an augmented dual of a cone is introduced. A special class of monotonically increasing sublinear functions is defined by using the elements of the augmented dual cone. Any closed cone possessing the separation property with its epsilon-conic neighborhood is shown to be approximated arbitrarily closely by a zero sublevel set of some function from this class. As an application, a simple and efficient scalarization technique for nonconvex vector optimization problems is suggested, and it is shown that any properly minimal point of a set in a Banach space can be calculated by minimizing a certain sublinear functional.Conference Object Citation - Scopus: 2Computing Efficient Solutions of Nonconvex Multi-Objective Problems Via Scalarization(2011) Kasimbeyli R.This paper presents a new method for scalarization of nonlinear multi-objective optimization problems. We introduce a special class of monotonically increasing sublinear scalarizing functions and show that the scalar optimization problem constructed by using these functions, enables to compute complete set of weakly efficient, efficient, and properly efficient solutions of multi-objective optimization problems without convexity and bound-edness conditions.Article Citation - WoS: 34Citation - Scopus: 42The Modified Subgradient Algorithm Based on Feasible Values(Taylor & Francis Ltd, 2009) Kasimbeyli̇, Refail; Ustun, Ozden; Rubinov, Alex M.In this article, we continue to study the modified subgradient (MSG) algorithm previously suggested by Gasimov for solving the sharp augmented Lagrangian dual problems. The most important features of this algorithm are those that guarantees a global optimum for a wide class of non-convex optimization problems, generates a strictly increasing sequence of dual values, a property which is not shared by the other subgradient methods and guarantees convergence. The main drawbacks of MSG algorithm, which are typical for many subgradient algorithms, are those that uses an unconstrained global minimum of the augmented Lagrangian function and requires knowing an approximate upper bound of the initial problem to update stepsize parameters. In this study we introduce a new algorithm based on the so-called feasible values and give convergence theorems. The new algorithm does not require to know the optimal value initially and seeks it iteratively beginning with an arbitrary number. It is not necessary to find a global minimum of the augmented Lagrangian for updating the stepsize parameters in the new algorithm. A collection of test problems are used to demonstrate the performance of the new algorithm.Article Citation - WoS: 52Citation - Scopus: 56Radial Epiderivatives and Set-Valued Optimization(Taylor & Francis Ltd, 2009) Kasimbeyli̇, RefailIn this article we study some important properties of the radial epiderivatives for single-valued and set-valued maps. The relationships between this kind of a derivative and weak subdifferentials and directional derivatives in the single-valued non-convex case has been established. For optimization problems with a single-valued and a set-valued objective function, necessary and sufficient optimality conditions based on the concept of the radial epiderivatives are proved without convexity conditions.Article Citation - WoS: 13Citation - Scopus: 15A Nonlinear Programming Technique To Compute a Tight Lower Bound for the Real Structured Singular Value(Springer, 2011) Yazici, Ahmet; Karamancioglu, Abdurrahman; Kasimbeyli̇, RefailThe real structured singular value (RSSV, or real mu) is a useful measure to analyze the robustness of linear systems subject to structured real parametric uncertainty, and surely a valuable design tool for the control systems engineers. We formulate the RSSV problem as a nonlinear programming problem and use a new computation technique, F-modified subgradient (F-MSG) algorithm, for its lower bound computation. The F-MSG algorithm can handle a large class of nonconvex optimization problems and requires no differentiability. The RSSV computation is a well known NP hard problem. There are several approaches that propose lower and upper bounds for the RSSV. However, with the existing approaches, the gap between the lower and upper bounds is large for many problems so that the benefit arising from usage of RSSV is reduced significantly. Although the F-MSG algorithm aims to solve the nonconvex programming problems exactly, its performance depends on the quality of the standard solvers used for solving subproblems arising at each iteration of the algorithm. In the case it does not find the optimal solution of the problem, due to its high performance, it practically produces a very tight lower bound. Considering that the RSSV problem can be discontinuous, it is found to provide a good fit to the problem. We also provide examples for demonstrating the validity of our approach.Research Project Veri Madenciliğinde Yeni Çok-sınıflı Sınıflandırma Yöntemleri ve Şirketlerin Finansal Özelliklerine Göre Derecelendirilmesi Problemine Uygulanması(2010) Kasimbeyli̇, Refail; Öztürk, Gürkan; Üstün, Özden[Abstract Not Available]Conference Object Citation - Scopus: 1Optimality Conditions Via Generalized Radial Epiderivatives in Nonconvex Set-Valued Optimization(Vilnius Gediminas Technical University, 2010) Kasimbeyli R.; Inceoglu G.In this paper, the generalized radial epiderivative for set-valued maps is introduced and its relationship to the radial epiderivative is investigated. Existence conditions for generalized radial epiderivatives are established and unified necessary and sufficient optimality condition in nonconvex setvalued optimization is derived in terms of the generalized radial epiderivative. © Izmir University of Economics, Turkey, 2010.