Payame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31303220180101Quasi-Gap and Gap Functions for Non-Smooth Multi-Objective Semi-Infinite Optimization Problemsتوابع شبهشکاف و شکاف برای مسائل نیمه-نامتناهی چندهدفه غیرهموار112671810.30473/coam.2020.50781.1133ENAtefehHassani BafraniDepartment of Mathematics, Payame Noor University, P.O. Box, 19395-3697, Tehran, Iran.0000-0003-2152-0606AliSadeghiehDepartment of Mathematics, Yazd branch, Islamic Azad University, Yazd, IranJournal Article20200108In this paper, we introduce and study some new single-valued gap functions for non-differentiable semi-infinite multiobjective optimization problems with locally Lipschitz data. Since one of the fundamental properties of gap function for optimization problems is its abilities in characterizing the solutions of the problem in question, then the essential properties of the newly introduced gap functions are established. All results are given in terms of the Clarke subdifferential.https://mathco.journals.pnu.ac.ir/article_6718_5931fe972a6feb3c383122e430f01982.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31303220180101A General Scalar-Valued Gap Function for Nonsmooth Multiobjective Semi-Infinite Programmingیک تابع شکاف حقیقی مقدار برای مسائل برنامه ریزی چند هدفی نیمه نامتناهی غیر هموار1326671910.30473/coam.2019.45495.1110ENAhmadRezayiDepartment of Mathematics, Payame Noor University, P.O. Box. 19395-3697, Tehran, IranJournal Article20190414For a nonsmooth multiobjective mathematical programming problem governed by infinitely many constraints, we define a new gap function that generalizes the definitions of this concept in other articles. Then, we characterize the efficient, weakly efficient, and properly efficient solutions of the problem utilizing this new gap function. Our results are based on $(\Phi,\rho)-$invexity, defined by Clarke subdifferential.https://mathco.journals.pnu.ac.ir/article_6719_59f10887b88b535008100a8c10d94722.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31303220180101MQ-Radial Basis Functions Center Nodes Selection with PROMETHEE Techniqueانتخاب نقاط مرکزی توابع پایه ای شعاعی با کمک تکنیک پرامیتی2747672010.30473/coam.2019.46609.1117ENFarhadHadinejadPhd of Operation Research Management, Allameh Tabataba'i University and Assistant professor, Imam Ali University, Tehran, IranSaeedKazemDepartment of Applied Mathematics, Amirkabir University of Technology, No. 424, Hafez Ave., 15914, Tehran, IranJournal Article20190531In this paper, we decide to select the best center nodes of radial basis functions by applying the Multiple Criteria Decision Making (MCDM) techniques. Two methods based on radial basis functions to approximate the solution of partial differential equation by using collocation method are applied. The first is based on the Kansa's approach, and the second is based on the Hermite interpolation. In addition, by choosing five sets of center nodes: Uniform grid, Cartesian, Chebyshev, Legendre and Legendre-Gauss-Lobato (LGL) as alternatives and achieving the error, the condition number of interpolation matrix and memory time as criteria, rating of cases with the help of PROMETHEE technique is obtained. In the end, the best center nodes and method is selected according to the rankings. This ranking shows that Hermite interpolation by using non-uniform nodes as center nodes is more suitable than Kansa's approach with each center node. https://mathco.journals.pnu.ac.ir/article_6720_2370abbdf97f6860667771e922775200.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31303220180101Characterization of Properly Efficient Solutions for Convex Multiobjective Programming with Nondifferentiable vanishing constraintsمشخصسازی جوابهای موثر سره برای مسائل چندهدفهی محدب با قیود غیرمشتقپذیر پوچشونده4958672110.30473/coam.2019.42442.1094ENJavadShaker ArdakaniDepartment of Mathematics, Payame Noor University (PNU), P.OBox, 19395-4679, Tehran, Iran.ShahriarFarahmand RadDepartment of Mathematics, Payame Noor University (PNU), P.OBox, 19395-4679, Tehran, Iran.0000-0003-1699-4962NaderKanziDepartment of Mathematics, Payame Noor University (PNU), P.OBox, 19395-4679, Tehran, Iran.0000-0003-0397-6415Journal Article20181118This paper studies the convex multiobjective optimization problem with vanishing constraints. We introduce a new constraint qualification for these problems, and then a necessary optimality condition for properly efficient solutions is presented. Finally by imposing some assumptions, we show that our necessary condition is also sufficient for proper efficiency. Our results are formulated in terms of convex subdifferential.https://mathco.journals.pnu.ac.ir/article_6721_67d7341f87c07e5b97e65519ca245268.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31303220180101Two Settings of the Dai-Liao Parameter Based on Modified Secant Equationsدو روش تنظیم پارامتر دای-لیاو بر اساس معادلات سکانت اصلاح شده5976672210.30473/coam.2020.46435.1116ENSaeedNezhadhoseinDepartment of Applied Mathematics, Payame Noor University, Tehran 193953697, IranSaharMohammadkhan SartipDepartment of Applied Mathematics, Payame Noor University, Tehran, 193953697, IranJournal Article20190528Following the setting of the Dai-Liao (DL) parameter in conjugate gradient (CG) methods, we introduce two new parameters based on the modified secant equation proposed by Li et al. (Comput. Optim. Appl. 202:523-539, 2007) with two approaches, which use an extended new conjugacy condition. The first is based on a modified descent three-term search direction, as the descent Hestenes-Stiefel CG method. The second is based on the quasi-Newton (QN) approach. Global convergence of the proposed methods for uniformly convex functions and general functions is proved. Numerical experiments are done on a set of test functions of the CUTEr collection and the results are compared with some well-known methods.https://mathco.journals.pnu.ac.ir/article_6722_a305748baa33534bbbd3520c72a3b261.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31303220180101A Fully Fuzzy Method of Network Data Envelopment Analysis for Assessing Revenue Efficiency Based on Ranking Functionsیک روش تمام فازی تحلیل پوششی دادههای شبکهای برای ارزیابی کارایی درآمد براساس توابع رتبهبندی7796672310.30473/coam.2019.46226.1115ENMohsenRostamy-MalkhalifehDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran0000-0001-6105-7674ElhamPoudinehDepartment of mathematics, kerman Branch, Islamic azad university, kerman.AliPayanDepartment of mathematics, zahedan branch, Islamic azad university, zahedan.Journal Article20190515The purpose of this paper is to evaluate the revenue efficiency in the fuzzy network data envelopment analysis. Precision measurements in real-world data are not practically possible, so assuming that data is crisp in solving problems is not a valid assumption. One way to deal with imprecise data is fuzzy data. In this paper, linear ranking functions are used to transform the full fuzzy efficiency model into a precise linear programming problem and, assuming triangular fuzzy numbers, the fuzzy revenue efficiency of decision makers is measured. In the end, a numerical example shows the proposed method.https://mathco.journals.pnu.ac.ir/article_6723_9de7a236e8cddde916d6cae4a73d36c6.pdf