Advances in induced optimal partition invariancy analysis in uni-parametric linear optimization
Nayyer
Mehanfar
Azarbaijan Shahid Madani University, Tabriz, Iran
author
Alireza
Ghaffari Hadigheh
Azarbaijan Shahid Madani University, Tabriz, Iran
author
text
article
2021
eng
In this study, we consider a family of uni-parametric linear optimization problems that the objective function, the right, and the left hand side of constraints are linearly perturbed with an identical parameter. We are interested in studying the effect of this variation on a given optimal solution and the behavior of the optimal value function on its domain. This problem has several applications, such as in linear time dynamical systems. A prototype example is provided in dynamical systems as a justification for the practicality of the study results. Based on the concept of induced optimal partition, we identify the intervals for the parameter value where optimal induced partitions are invariant. We show that the optimal value function is piecewise fractional continuous in the interior of its domain, while it is not necessarily to be continuous at the endpoints. Some concrete examples depict the results of the analysis.
Journal of Mathematical Modeling
University of Guilan
2345-394X
9
v.
2
no.
2021
145
172
https://jmm.guilan.ac.ir/article_4667_625d5dd6ff09861f3b9a66dc0d60e388.pdf
dx.doi.org/10.22124/jmm.2021.4667
Unified ball convergence of third and fourth convergence order algorithms under $\omega-$continuity conditions
Gus
Argyros
Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA
author
Michael
Argyros
Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA
author
Ioannis
Argyros
Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA
author
Santhosh
George
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025
author
text
article
2021
eng
There is a plethora of third and fourth convergence order algorithms for solving Banach space valued equations. These orders are shown under conditions on higher than one derivatives not appearing on these algorithms. Moreover, error estimations on the distances involved or uniqueness of the solution results if given at all are also based on the existence of high order derivatives. But these problems limit the applicability of the algorithms. That is why we address all these problems under conditions only on the first derivative that appear in these algorithms. Our analysis includes computable error estimations as well as uniqueness results based on $\omega-$ continuity conditions on the Fr\'echet derivative of the operator involved.
Journal of Mathematical Modeling
University of Guilan
2345-394X
9
v.
2
no.
2021
173
183
https://jmm.guilan.ac.ir/article_4310_8e463016ecf1a718f19b0629b8fd7291.pdf
dx.doi.org/10.22124/jmm.2020.17556.1513
Solution of Kawahara equation using a predictor-corrector and RBF-QR method
Zahra
Dehghan
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
author
Jalil
Rashidinia
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
author
text
article
2021
eng
Two different methods based on radial basis functions (RBFs) for one-dimensional Kawahara equation are presented. In the first one, we use MQ-RBF with predictor-corrector scheme. Then the statistical tool LOOCV is implemented for selecting good value of shape parameter. In the second one a different scheme is constructed for time and then the RBF-QR method is implemented. In the both of two approaches, the Not-a-Knot method is used to improve the accuracy at the boundaries. The purpose of this paper is to devot suitable strategies to obtain more accurate and efficient solutions specially for arising fifth order time-dependent nonlinear equations comparing with the results from the relevant papers.
Journal of Mathematical Modeling
University of Guilan
2345-394X
9
v.
2
no.
2021
185
199
https://jmm.guilan.ac.ir/article_4311_f6504d7ccaf8049edc04226d04a09978.pdf
dx.doi.org/10.22124/jmm.2020.17221.1497
Solution of nonlinear Volterra and Fredholm integro-differential equations by the rational Haar wavelet
Majid
Erfanian
Department of Science, School of Mathematical Sciences, University of Zabol, Iran
author
Hamed
Zeidabadi
Faculty of Engineering, Sabzevar University of New Technology, Sabzevar, Iran
author
text
article
2021
eng
We successively apply the rational Haar wavelet to solve the nonlinear Volterra integro-differential equations and nonlinear Fredholm integro-differential equations. Using the Banach fixed point theorem for these equations, we prove the convergence. In this method, no numerical integration is used. Numerical results are presented to show the effectiveness of this method.
Journal of Mathematical Modeling
University of Guilan
2345-394X
9
v.
2
no.
2021
201
213
https://jmm.guilan.ac.ir/article_4312_793f71f4174613da9dc51675d4e83fb2.pdf
dx.doi.org/10.22124/jmm.2020.16051.1404
Flow shop scheduling under Time-Of-Use electricity tariffs using fuzzy multi-objective linear programming approach
Seyed Amin
Badri
Department of Industrial Engineering, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran
author
Allahyar
Daghbandan
Department of Chemical Engineering, Faculty of Engineering, University of Guilan, Rasht, Iran
author
Zahra
Aghabeiginiyay Fatalaki
Department of Industrial Engineering, Kooshyar higher education institute, Rasht, Iran
author
Mohammad
Mirzazadeh
Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran
author
text
article
2021
eng
Given the reduction of non-renewable energy resources and increase of energy costs during recent years, developing an efficient scheduling model considering energy consumption is necessary in manufacturing systems. This paper is dedicated to flow shop scheduling problem under Time-Of-Use electricity tariffs. In this regard, a bi-objective mixed-integer programming model is formulated for the problem. Two objectives, namely, the minimization of the total electricity cost and the sum of earliness and tardiness of jobs, are considered simultaneously. The bi-objective model is converted into an equivalent single objective linear programming model using fuzzy multi-objective programming approach. The CPLEX solver in GAMS software is used to solve the proposed model for an instance. The numerical example shows that the proposed model is reasonable and applicable.
Journal of Mathematical Modeling
University of Guilan
2345-394X
9
v.
2
no.
2021
215
227
https://jmm.guilan.ac.ir/article_4335_f1bc25e87d5e943ac1d33bf41f98cf87.pdf
dx.doi.org/10.22124/jmm.2020.16104.1406
Solution of a certain problem of scattering by using of the maximum entropy principle
Alexander
Balandin
Matrosov Institute for Systems Dynamics and Control
Theory, Siberian Branch, Russian Academy of Sciences,
134 Lermontov str., Irkutsk-33, 664033, Russia
author
text
article
2021
eng
This paper studies a problem of inverse scattering on the basis of maximum entropy principle. The advantage of the method implies maximization of the entropy functional, what is the main condition and the scattering data and any a priory information are considered as constraints. This rephrasing of the problem leads to significant simplifications, since the entropy functional is known to be concave. Other peculiar properties of the method include his stability to various kinds of artifacts and adaptability to various schemes of measurement.
Journal of Mathematical Modeling
University of Guilan
2345-394X
9
v.
2
no.
2021
229
238
https://jmm.guilan.ac.ir/article_4344_bfb58334cd1c49a3d95027d821efa550.pdf
dx.doi.org/10.22124/jmm.2020.17714.1526
Augmented and deflated CMRH method for solving nonsymmetric linear systems
Zohreh
Ramezani
Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Iran
author
Faezeh
Toutounian
Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Iran
author
text
article
2021
eng
The CMRH (Changing Minimal Residual method based on the Hessenberg process) is an iterative method for solving nonsymmetric linear systems. The method generates a Krylov subspace in which an approximate solution is determined. The CMRH method is generally used with restarting to reduce the storage. Restarting often slows down the convergence. In this paper we present augmentation and deflation techniques for accelerating the convergence of the restarted CMRH method. Augmentation adds a subspace to the Krylov subspace, while deflation removes certain parts from the operator. Numerical experiments show that the new algorithms can be more efficient compared with CMRH method.
Journal of Mathematical Modeling
University of Guilan
2345-394X
9
v.
2
no.
2021
239
256
https://jmm.guilan.ac.ir/article_4350_a9625261ff4043bb048276bc975214e1.pdf
dx.doi.org/10.22124/jmm.2020.17024.1511
Denumerably many positive solutions for singular iterative system of fractional differential equation with R-L fractional integral boundary conditions
Kapula
Rajendra Prasad
Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, 530003, India
author
Mahammad
Khuddush
Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, 530003, India
author
Mahanty
Rashmita
Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, 530003, India
author
text
article
2021
eng
In this paper, we establish the existence of denumerably many positive solutions for singular iterative system of fractional order boundary value problem involving Riemann--Liouville integral boundary conditions with increasing homeomorphism and positive homomorphism operator by using H\"{o}lder's inequality and Krasnoselskii's cone fixed point theorem in a Banach space.
Journal of Mathematical Modeling
University of Guilan
2345-394X
9
v.
2
no.
2021
257
275
https://jmm.guilan.ac.ir/article_4351_fec198a0464282cff08461adf34a82c2.pdf
dx.doi.org/10.22124/jmm.2020.16598.1441
Optimal control of time delay Fredholm integro-differential equations
Maryam
Alipour
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
author
Samaneh
Soradi-Zeid
Faculty of Industry and Mining (khash), University of Sistan and Baluchestan, Zahedan, Iran
author
text
article
2021
eng
This paper is devoted to solve a set of non-linear optimal control problems which are touched with time-delay Fredholm integro-differential equations. The serious objective of this work is to contribute an appropriate direct scheme for solving these problems. The technique used in this paper is based upon the Dickson polynomials and collocation points. Getting through the solutions, the states and controls variables can be approximated with Dickson polynomials. Therefore, the optimal control problem with time-delay integro-differential equation transforms into a system of algebraic equations that by solving it, we can obtain the unknown coefficients of the main problem. The residual error estimation of this technique is also investigated. Accuracy amount of the absolute errors have been studied for the performance of this method by solving several non-trivial examples.
Journal of Mathematical Modeling
University of Guilan
2345-394X
9
v.
2
no.
2021
277
291
https://jmm.guilan.ac.ir/article_4365_b1895f71be4e68731cb49dddd88a29e2.pdf
dx.doi.org/10.22124/jmm.2020.17213.1496
Distribution of eigenvalues for sub-skewtriagonal Hankel matrices
Maryam
Shams Solary
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran
author
text
article
2021
eng
We investigate the eigenvalue distribution of banded Hankel matrices with non-zero skew diagonals. This work uses push-forward of an arcsine density, block structures and generating functions. Our analysis is done by a combination of Chebyshev polynomials, Laplacian determinant expansion and mathematical induction.
Journal of Mathematical Modeling
University of Guilan
2345-394X
9
v.
2
no.
2021
293
302
https://jmm.guilan.ac.ir/article_4441_f1f2502a7fc4561b14fff3458ffdbcc6.pdf
dx.doi.org/10.22124/jmm.2020.17283.1499
Introduction of the numerical methods in quantum calculus with uncertainty
Zahra
Noeiaghdam
Department of Mathematics, Shahed University, Tehran, Iran
author
Morteza
Rahmani
Department of Mathematics, Shahed University, Tehran, Iran & Faculty of Basic and Advanced Technologies in Biology, University of Science and Culture, Tehran, Iran
author
Tofigh
Allahviranloo
Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey & Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
author
text
article
2021
eng
The aim of this study is the introduction of the numerical methods for solving the fuzzy $q$-differential equations that many real life problems can be modelized in the form of these equations. $q$-Taylor's expansion method is among important and famous methods for solving these problems. In this paper, applications of the fuzzy $q$-Taylor's expansion, the fuzzy local $q$-Taylor's expansion and the fuzzy $q$-Euler's method, based on the generalized Hukuhara $q$-differentiability are illustrated which are two numerical methods for finding approximate solution of the fuzzy initial value $q$-problems (for short FIVq-Ps).
Journal of Mathematical Modeling
University of Guilan
2345-394X
9
v.
2
no.
2021
303
322
https://jmm.guilan.ac.ir/article_4456_fabfb14b81d47fdae669a51bc70a9df3.pdf
dx.doi.org/10.22124/jmm.2020.17822.1534
Note to the convergence of minimum residual HSS method
Arezo
Ameri
Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran
author
Fatemeh
Panjeh Ali Beik
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
author
text
article
2021
eng
The minimum residual HSS (MRHSS) method is proposed in [BIT Numerical Mathematics, 59 (2019) 299--319] and its convergence analysis is proved under a certain condition. More recently in [Appl. Math. Lett. 94 (2019) 210--216], an alternative version of MRHSS is presented which converges unconditionally. In general, as the second approach works with a weighted inner product, it consumes more CPU time than MRHSS to converge. In the current work, we revisit the convergence analysis of the MRHSS method using a different strategy and state the convergence result for general two-step iterative schemes. It turns out that a special choice of parameters in the MRHSS results in an unconditionally convergent method without using a weighted inner product. Numerical experiments confirm the validity of established results.
Journal of Mathematical Modeling
University of Guilan
2345-394X
9
v.
2
no.
2021
323
330
https://jmm.guilan.ac.ir/article_4457_ff5133b3aab29d48f60bd3c444cb7bfd.pdf
dx.doi.org/10.22124/jmm.2020.18109.1559