ORIGINAL_ARTICLE
Advances in induced optimal partition invariancy analysis in uni-parametric linear optimization
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.
https://jmm.guilan.ac.ir/article_4667_625d5dd6ff09861f3b9a66dc0d60e388.pdf
2021-05-01
145
172
10.22124/jmm.2021.4667
Uni-parameter linear optimization
Induced optimal partition invariancy analysis
change point
Moore-Penrose inverse
Realization theory
Nayyer
Mehanfar
mehanfar.n@azaruniv.ac.ir
1
Azarbaijan Shahid Madani University, Tabriz, Iran
AUTHOR
Alireza
Ghaffari Hadigheh
hadigheha@azaruniv.ac.ir
2
Azarbaijan Shahid Madani University, Tabriz, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Unified ball convergence of third and fourth convergence order algorithms under $\omega-$continuity conditions
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.
https://jmm.guilan.ac.ir/article_4310_8e463016ecf1a718f19b0629b8fd7291.pdf
2021-05-01
173
183
10.22124/jmm.2020.17556.1513
$omega-$ continuity
ball of convergence
Algorithm
Gus
Argyros
gus.argyros@cameron.edu
1
Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA
AUTHOR
Michael
Argyros
michael.argyros@cameron.edu
2
Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA
AUTHOR
Ioannis
Argyros
iargyros@cameron.edu
3
Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA
AUTHOR
Santhosh
George
sgeorge@nitk.edu.in
4
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025
LEAD_AUTHOR
ORIGINAL_ARTICLE
Solution of Kawahara equation using a predictor-corrector and RBF-QR method
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.
https://jmm.guilan.ac.ir/article_4311_f6504d7ccaf8049edc04226d04a09978.pdf
2021-05-01
185
199
10.22124/jmm.2020.17221.1497
Kawahara equation
multiquadric Radial basis functions
theta-weighted scheme
RBF-QR
LOOCV strategy
Zahra
Dehghan
kntu.dehghan@gmail.com
1
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
AUTHOR
Jalil
Rashidinia
rashidinia@iust.ac.ir
2
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Solution of nonlinear Volterra and Fredholm integro-differential equations by the rational Haar wavelet
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.
https://jmm.guilan.ac.ir/article_4312_793f71f4174613da9dc51675d4e83fb2.pdf
2021-05-01
201
213
10.22124/jmm.2020.16051.1404
Fixed point Banach theorem
nonlinear
Volterra
Fredholm
integro-differential
Haar wavelet
Convergence
Majid
Erfanian
erfaniyan@uoz.ac.ir
1
Department of Science, School of Mathematical Sciences, University of Zabol, Iran
LEAD_AUTHOR
Hamed
Zeidabadi
h.zeidabadi@yahoo.com
2
Faculty of Engineering, Sabzevar University of New Technology, Sabzevar, Iran
AUTHOR
ORIGINAL_ARTICLE
Flow shop scheduling under Time-Of-Use electricity tariffs using fuzzy multi-objective linear programming approach
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.
https://jmm.guilan.ac.ir/article_4335_f1bc25e87d5e943ac1d33bf41f98cf87.pdf
2021-05-01
215
227
10.22124/jmm.2020.16104.1406
mixed-integer programming
bi-objective model
electricity price
earliness
tardiness
Seyed Amin
Badri
badri@guilan.ac.ir
1
Department of Industrial Engineering, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran
LEAD_AUTHOR
Allahyar
Daghbandan
daghbandan@guilan.ac.ir
2
Department of Chemical Engineering, Faculty of Engineering, University of Guilan, Rasht, Iran
AUTHOR
Zahra
Aghabeiginiyay Fatalaki
zahra.aghabeigi1371@gmail.com
3
Department of Industrial Engineering, Kooshyar higher education institute, Rasht, Iran
AUTHOR
Mohammad
Mirzazadeh
mirzazadehs2@guilan.ac.ir
4
Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran
AUTHOR
ORIGINAL_ARTICLE
Solution of a certain problem of scattering by using of the maximum entropy principle
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.
https://jmm.guilan.ac.ir/article_4344_bfb58334cd1c49a3d95027d821efa550.pdf
2021-05-01
229
238
10.22124/jmm.2020.17714.1526
inverse problems
maximum entropy
cone ray transform
computerized tomography
Alexander
Balandin
balandin@icc.ru
1
Matrosov Institute for Systems Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, 134 Lermontov str., Irkutsk-33, 664033, Russia
LEAD_AUTHOR
ORIGINAL_ARTICLE
Augmented and deflated CMRH method for solving nonsymmetric linear systems
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.
https://jmm.guilan.ac.ir/article_4350_a9625261ff4043bb048276bc975214e1.pdf
2021-05-01
239
256
10.22124/jmm.2020.17024.1511
Krylov subspace methods
augmentation
deflation
CMRH method
GMRES method
harmonic Ritz values
Zohreh
Ramezani
z_ramezani1367@yahoo.com
1
Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Iran
AUTHOR
Faezeh
Toutounian
toutouni@math.um.ac.ir
2
Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Denumerably many positive solutions for singular iterative system of fractional differential equation with R-L fractional integral boundary conditions
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.
https://jmm.guilan.ac.ir/article_4351_fec198a0464282cff08461adf34a82c2.pdf
2021-05-01
257
275
10.22124/jmm.2020.16598.1441
Denumerable
positive solutions
fractional derivative
homeomorphism
homomorphism
Fixed point theorem
Kapula
Rajendra Prasad
rajendra92@rediffmail.com
1
Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, 530003, India
AUTHOR
Mahammad
Khuddush
khuddush89@gmail.com
2
Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, 530003, India
LEAD_AUTHOR
Mahanty
Rashmita
rashmita.mahanty@gmail.com
3
Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, 530003, India
AUTHOR
ORIGINAL_ARTICLE
Optimal control of time delay Fredholm integro-differential equations
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.
https://jmm.guilan.ac.ir/article_4365_b1895f71be4e68731cb49dddd88a29e2.pdf
2021-05-01
277
291
10.22124/jmm.2020.17213.1496
Optimal control problems
Dickson polynomials
Time-delay equation
Fredholm integrao-differential equation
collocation points
Maryam
Alipour
m.alipour@math.usb.ac.ir
1
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
AUTHOR
Samaneh
Soradi-Zeid
soradizeid@eng.usb.ac.ir
2
Faculty of Industry and Mining (khash), University of Sistan and Baluchestan, Zahedan, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Distribution of eigenvalues for sub-skewtriagonal Hankel matrices
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.
https://jmm.guilan.ac.ir/article_4441_f1f2502a7fc4561b14fff3458ffdbcc6.pdf
2021-05-01
293
302
10.22124/jmm.2020.17283.1499
Hankel
eigenvalue
Distribution
generating function
Maryam
Shams Solary
shamssolary@pnu.ac.ir
1
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Introduction of the numerical methods in quantum calculus with uncertainty
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).
https://jmm.guilan.ac.ir/article_4456_fabfb14b81d47fdae669a51bc70a9df3.pdf
2021-05-01
303
322
10.22124/jmm.2020.17822.1534
Generalized Hukuhara $q$-derivative
fuzzy $q$-Taylor's theorem
fuzzy local $q$-Taylor's expansion
fuzzy $q$-Euler's method
Zahra
Noeiaghdam
zahra.noie@yahoo.com
1
Department of Mathematics, Shahed University, Tehran, Iran
AUTHOR
Morteza
Rahmani
rahmanimr@yahoo.com
2
Department of Mathematics, Shahed University, Tehran, Iran & Faculty of Basic and Advanced Technologies in Biology, University of Science and Culture, Tehran, Iran
LEAD_AUTHOR
Tofigh
Allahviranloo
allahviranloo@yahoo.com
3
Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey & Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
AUTHOR
ORIGINAL_ARTICLE
Note to the convergence of minimum residual HSS method
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.
https://jmm.guilan.ac.ir/article_4457_ff5133b3aab29d48f60bd3c444cb7bfd.pdf
2021-05-01
323
330
10.22124/jmm.2020.18109.1559
Minimum residual technique
Hermitian and skew-Hermitian splitting
two-step iterative method
Convergence
Arezo
Ameri
arezoameri20@gmail.com
1
Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran
AUTHOR
Fatemeh
Panjeh Ali Beik
f.beik@vru.ac.ir
2
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
LEAD_AUTHOR