Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69777120170401Computing the eigenvalues of fourth order Sturm-Liouville problems with Lie Group methodمحاسبه ی مقادیر ویژه ی مسائل اشتورم-لیوویل مرتبه ی چهار به روش گروه لی1122449710.22067/ijnao.v7i1.44788ENH.MirzaeiFaculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.Journal Article19700101In this paper, we formulate the fourth order Sturm-Liouville problem (FSLP) as a Lie group matrix differential equation. By solving this ma- trix diﬀerential equation by Lie group Magnus expansion, we compute the eigenvalues of the FSLP. The Magnus expansion is an inﬁnite series of multiple integrals of Lie brackets. The approximation is, in fact, the truncation of Magnus expansion and a Gaussian quadrature are used to evaluate the integrals. Finally, some numerical examples are given.https://ijnao.um.ac.ir/article_24497_c20e2e247f1710e92e7019be45f4de2e.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69777120170401Stability Analysis of Conformable Fractional Systemsتحلیل پایداری سیستم های کسری منطبق شدنی13322450310.22067/ijnao.v7i1.46917ENH.RezazadehDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran.H.AminikhahDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran.A.H.Refahi SheikhaniDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Islamic Azad University, Lahijan Branch, P.O. Box 1616, Lahijan, Iran.Journal Article19700101 In this paper, we investigate stability analysis of fractional diﬀerential systems equipped with the conformable fractional derivatives. Some stability conditions of fractional differential systems are proposed by applying the fractional exponential function and the fractional Laplace transform. Moreover, we check the stability of conformable fractional Lotka-Volterra system with the multi-step homotopy perturbation method to demonstrate the efficiency and eﬀectiveness of the proposed procedure.https://ijnao.um.ac.ir/article_24503_4692483d59ff23bf6f7d18f6ad279fee.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69777120170401A parametric iteration method for solving Lane-Emden type equationsروش تکرار پارامتریک بهینه برای حل معادلات نوع Lane-Emden33462450610.22067/ijnao.v7i1.39519ENR.ChaharpashlouDepartment of Basic Sciences, Jundi-Shapur University of Technology, Dezful, Iran.Journal Article19700101In this paper, an analytical method called the parametric iteration method (PIM) is presented for solving the second-order singular IVPs of Lane-Emden type, and its local convergence is discussed. Since it is often useful to have an approximate analytical solution to describe the Lane-Emden type equa- tions, especially for ones where the closed-form solutions do not exist at all, therefore, an eﬀective improvement of the PIM is further proposed that is ca- pable of obtaining an approximate analytical solution. The improved PIM is ﬁnally treated as an algorithm in a sequence of intervals for ﬁnding accurate approximate solutions of the nonlinear Lane-Emden type equations. Also, we show how to identify an approximate optimal value of the convergence accelerating parameter within the frame of the method. Some examples are given to demonstrate the eﬃciency and accuracy of the proposed method.https://ijnao.um.ac.ir/article_24506_20eb4f21f86c9f6d57ef73d3c0a2f835.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69777120170401The concept of B-efficient solution in fair multiobjective optimization problems47642451110.22067/ijnao.v7i1.43960END.ForoutanniaDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.A.MahmodinejadDepartment of Mathematics, Sirjan University of Technology, Sirjan, Iran.Journal Article19700101A problem that sometimes occurs in multiobjective optimization is the existence of a large set of fairly effcient solutions. Hence, the decision making based on selecting a unique preferred solution is diffcult. Considering models with fair B-effciency relieves some of the burden from the decision maker by shrinking the solution set, since the set of fairly B-eﬃcient solutions is contained within the set of fairly effcient solutions for the same problem. In this paper, ﬁrst some theoretical and practical aspects of fairly B- effcient solutions are discussed. Then, some scalarization techniques are developed to generate fairly B-effcient solutions.https://ijnao.um.ac.ir/article_24511_f63d7613e52d892f1b1e21b32d8b4ed8.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69777120170401Efficient methods for goal square Weber location problemمساله مکانیابی وبر مربعی آرمانی65822451710.22067/ijnao.v7i1.52961ENJ.FathaliDepartment of Mathematics, Shahrood University of Technology, University Blvd., Shahrood, Iran.0000-0003-1397-8529A.JamalianDepartment of Computer Scince, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.Journal Article19700101In this paper, we consider a special case of Weber location problem which we call goal location problem. The Weber location problem asks to ﬁnd location of a point in the plane such that the sum of weighted distances between this point and n existing points is minimized. In the goal location problem each existing point Pi has a relevant radius ri and it’s ideal for us to locate a new facility on the distance ri from Pi for i = 1, ..., n. Since in the most instances there does not exist the location of a new facility such that its distance to each point Pi be exactly equal to ri. So we try to minimize the sum of the weighted square errors. We consider the case that the distances in the plane are measured by the Euclidean norm. We propose a Weiszfeld like algorithm for solving the problem and also we use two modiﬁcations of particle swarm optimization method for solving this problem. Finally the results of these algorithms are compared with results of BSSS algorithm.https://ijnao.um.ac.ir/article_24517_bf85231e6bf925fd47b5f44be9f845e2.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69777120170401A Reliable Approach for Terminating the GA Optimization Method831062452210.22067/ijnao.v7i1.48652ENL.Lotfi KatooliDepartment of Chemical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, IranA.ShahsavandDepartment of Chemical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, IranJournal Article19700101Genetic algorithm (GA) has been extensively used in recent decades to solve many optimization problems in various ﬁelds of science and engineering. In most cases, the number of iterations is the only criterion which is used to stop the GA. In practice, this criterion will lead to prolong execution times to ensure proper solution. A novel approach is presented in this article as the approximate number of decisive iterations (ANDI ) which can be used to successfully terminate the GA optimization method with minimum execution time. Two simple correlations are presented which relate the new parameter (ANDI ) with approximate degrees of freedom (Adf ) of the merit function at hand. For complex merit functions, a linear smoother (such as Regularization network) can be used to estimate the required Adf. Four illustrative case studies are used to successfully validate the proposed approach by effectively ﬁnding the optimum point by using to the presented correlation. The linear correlation is more preferable because it is much simpler to use and the horizontal axis represents the approximate (not exact) degrees of freedom. It was also clearly shown that the Regularization Networks can successfully ﬁlter out the noise and mimic the true hyper-surface underlying a bunch of noisy data set.https://ijnao.um.ac.ir/article_24522_2fc0c38bd93842983946ab2276baecf0.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69777120170401Alternating direction method of multipliers for the extended trust region subproblemروش جهت متناوب ضرایب برای زیر مساله ناحیه اطمینان توسیع یافته1071172453110.22067/ijnao.v7i1.52283ENM.SalahiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.A.TaatiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.Journal Article19700101The extended trust region subproblem has been the focus of several research recently. Under various assumptions, strong duality and certain SOCP/SDP relaxations have been proposed for several classes of it. Due to its importance, in this paper, without any assumption on the problem, we apply the widely used alternating direction method of multipliers (ADMM) to solve it. The convergence of ADMM iterations to the ﬁrst order stationary conditions is established. On several classes of test problems, the quality of the solution obtained by the ADMM for medium scale problems is compared with the SOCP/SDP relaxation. Moreover, the applicability of the method for solving large scale problems is shown by solving several large instances.https://ijnao.um.ac.ir/article_24531_4133f8eb686d855b923976b49be28ebb.pdf