eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-01
9
2
1
7
10.22075/ijnaa.2017.415.1060
3490
Numerical algorithm for discrete barrier option pricing in a Black-Scholes model with stationary process
Rahman Farnoosh
hr_rezazadeh@mathdep.iust.ac.ir
1
Hamidreza Rezazadeh
rfarnoosh@iust.ac.ir
2
Amirhossein Sobhani
3
Masoud Hasanpour
hr_rezazadeh@yahoo.com
4
School of Mathematics, Iran University of Science and Technology, 16844 Tehran, Iran
Department of Mathematics, Islamic Azad University Karaj Branch
School of Mathematics, Iran University of Science and Technology, 16844 Tehran, Iran
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
In this article, we propose a numerical algorithm for computing price of discrete single and double barrier option under the <span>emph</span>{Black-<span>Scholes</span>} model. In virtue of some general transformations, the partial differential equations of option pricing in different monitoring dates are converted into simple diffusion equations. The present method is fast compared to alternative numerical methods presented in previous papers.
https://ijnaa.semnan.ac.ir/article_3490_e9dc9637e7faed498b3c25279b93fb11.pdf
Discrete Barrier Option
emph{Black-Scholes} Model
Constant Parameters
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-01
9
2
9
19
10.22075/ijnaa.2018.11633.1579
3491
Symmetric Rogers-Hölder's inequalities on diamond-α calculus
Sajid Iqbal
sajid_uos2000@yahoo.com
1
Muhammad Jibril Shahab Sahir
jibrielshahab@gmail.com
2
Muhammad Samraiz
msamraiz@uos.edu.pk
3
Department of Mathematics, University of Sargodha, Sub-Campus Mianwali
Department of Mathematics, University of Sargodha, Sub-Campus Bhakkar, Bhakkar, Pakistan
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
We present symmetric Rogers--Hö<span>lder's</span> inequalities on time scales when <span>$frac{1}{p}+frac{1}{q}+frac{1}{r}=0$</span> and <span>$frac{r}{p}+frac{r}{q}$</span> is not necessarily equal to <span>$1$</span> where <span>$p,$</span> <span>$q$</span> and <span>$r$</span> are <span>nonzero</span> real numbers.
https://ijnaa.semnan.ac.ir/article_3491_99dcc0be916ae65dbe4e4d984b19863b.pdf
Diamond-$alpha$ integral
Rogers-Hölder's inequalities
time scales
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-06
9
2
21
31
10.22075/ijnaa.2018.12625.1641
3492
Nonlinear dynamic of the multicellular chopper
Djondin Philippe
pdjondine@yahoo.fr
1
Jean-Pierre Barbot
barbot@ensea.fr
2
Department of Physics, Faculty of Science, The University of Ngaound'er'e, P.O. Box 454, Ngaound'er'e, Cameroon
ECS-Lab, EA3649, ENSEA, Cergy Cedex, Cergy--Pontoise 95014, France, Laboratoire QUARTZ EA 7393
In this paper, the dynamics of multicellular chopper are considered. The model is described by a continuous time three--dimensional autonomous system. Some basic dynamical properties such as <span>Poincar</span><span>'e</span> mapping, power spectrum and chaotic <span>behaviors</span> are studied. Analysis results show that this system has complex dynamics with some interesting characteristics.
https://ijnaa.semnan.ac.ir/article_3492_56510194ff66e9a2f31ddc19c6a3b579.pdf
Chaos
multicellular chopper
dynamical properties
chaotic attractor
routes to chaos
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-12
9
2
33
45
10.22075/ijnaa.2018.1496.1386
3493
An existence result for n^{th}-order nonlinear fractional differential equations
Ali Benlabbes
alibenlabbes@hotmail.fr
1
Maamar Benbachir
mbenbachir2001@gmail.com
2
Mustapha Lakrib
m.lakrib@univ-sba.dz
3
Faculty of Sciences and Technology, Tahri Mohammed University, Bechar, Algeria
Faculty of Sciences and Technology, Djilali Bounaama University, Khemis-Miliana, Algeria
Laboratory of Mathematics, Djillali Liab\`{e}s University, Sidi Bel Abb\`es, Algeria
In this paper, we investigate the existence of solutions of some three-point boundary value problems for n-th order nonlinear fractional differential equations with higher boundary conditions by using a fixed point theorem on cones.
https://ijnaa.semnan.ac.ir/article_3493_42f30dd586fe63bb05aaae937088de0f.pdf
Caputo fractional derivative
three-point boundary value problem
fixed point theorem on cones
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-14
9
2
47
57
10.22075/ijnaa.2017.1538.1402
3494
Multiple solutions of a nonlinear reactive transport model using least square pseudo-spectral collocation method
Elyas Shivanian
e_shivanian@yahoo.com
1
Saeid Abbasbandy
abbasbandy@yahoo.com
2
Department of Applied Mathematics, Faculty of Basic Science, Imam Khomeini International University, Qazvin 34149-16818, Iran
Department of Applied Mathematics, Faculty of Basic Science, Imam Khomeini International University, Qazvin 34149-16818, Iran
The recognition and the calculation of all branches of solutions of the nonlinear boundary value problems is difficult obviously. The complexity of this issue goes back to the being nonlinearity of the problem. Regarding this matter, this paper considers steady state reactive transport model which does not have exact closed-form solution and discovers existence of dual or triple solutions in some cases using a new hybrid method based on pseudo-spectral collocation in the sense of least square method. Furthermore, the method usages Picard iteration and Newton method to treat nonlinear term in order to obtain unique and multiple solutions of the problem, respectively.
https://ijnaa.semnan.ac.ir/article_3494_4c905e7d18378893866322225fe54d53.pdf
Pseudo-spectral collocation method
Least square method
Newton iteration method
Picard iteration
Chebyshev-Gauss-Lobatto points
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-10
9
2
59
69
10.22075/ijnaa.2018.1589.1417
3495
Coefficient bounds for a new class of univalent functions involving Salagean operator and the modified Sigmoid function
Olubunmi Fadipe-Joseph
famelov@gmail.com
1
W. Ademosu
tinuadewuraola114@gmail.com
2
G. Murugusundaramoorthy
gmsmoorthy@yahoo.com
3
Department of Mathematics, University of Ilorin, P.M.B 1515, Ilorin, Nigeria
Department of Mathematics,Statistics and Computer Sci., Federal University of Agriculture, P.M.B 2373, Makurdi, Nigeria
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Deemed to be University, Vellore-632 014, India
We define a new subclass of univalent function based on Salagean differential operator and obtained the initial Taylor coefficients using the techniques of Briot-Bouquet differential subordination in association with the modified sigmoid function. Further we obtain the classical Fekete-Szego inequality results.
https://ijnaa.semnan.ac.ir/article_3495_185b784a98886e32bb1fbec5c5ab08ec.pdf
Univalent functions
Briot-Bouquet differential equation
Integral Operator
Sv{a}lv{a}gean differential operator
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-11
9
2
71
84
10.22075/ijnaa.2018.1644.1432
3496
Generalized multivalued $F$-contractions on non-complete metric spaces
Hamid Baghani
h.baghani@gmail.com
1
Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran
In this paper, we explain a new generalized <span>contractive</span> condition for multivalued mappings and prove a fixed point theorem in metric spaces (not necessary complete) which extends some well-known results in the literature. Finally, as an application, we prove that a multivalued function satisfying a general linear functional inclusion admits a unique selection fulfilling the corresponding functional equation.
https://ijnaa.semnan.ac.ir/article_3496_4b64c826687d159161940de7dcd0b715.pdf
Fixed point theorem
Weakly Picard operator
O-complete metric space
Selections of multivalued functions
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-14
9
2
85
109
10.22075/ijnaa.2018.868.1157
3503
Fixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces
Hemant Kumar Nashine
drhknashine@gmail.com
1
Atul Kumar Sharma
hemantnashine@gmail.com
2
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, TN, INDIA
Department of Mathematics, Lakhmi Chand Institute of Technology, Bilaspur-495001,(Chhattisgarh), India
We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly <span>contractive</span> condition in partially ordered complete <span>$G$</span>-metric spaces. Some examples are furnished to illustrate the <span>useability</span> of our main results. At the end, an application is presented to the study of existence and uniqueness of solutions for a boundary value problem for certain second order ODE and the respective integral equation.
https://ijnaa.semnan.ac.ir/article_3503_49b512c18a4eb3d87910b9125ccef4dc.pdf
$G$-metric space
Weakly contraction condition
Altering distance function
Compatible mappings
Coincidence point
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-13
9
2
111
116
10.22075/ijnaa.2018.3510
3510
A class of certain properties of approximately n-multiplicative maps between locally multiplicatively convex algebras
Zohre Heidarpour
heidarpor86@yahoo.com
1
Esmaeil Ansari-Piri
eansaripiri@gmail.com
2
Hamid Shayanpour
h.shayanpour@sci.sku.ac.ir
3
Ali Zohri
alizohri@gmail.com
4
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Shahrekord, P. O. Box 88186-34141, Shahrekord, Iran
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran
We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps. We prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous. We also study the relationship between approximately multiplicative linear functionals and approximately n-multiplicative linear functionals.
https://ijnaa.semnan.ac.ir/article_3510_7ba671699220e09a6a455a6e8874ad8b.pdf
Almost multiplicative maps
n-homomorphism maps
approximately n-multiplicatives
LMC algebras
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-15
9
2
117
129
10.22075/ijnaa.2017.1312.1324
3511
Strict fixed points of '{C}iri'{c}-generalized weak quasicontractive multi-valued mappings of integral type
Babak Mohammadi
babakmohammadi28@yahoo.com
1
Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran
Many authors such as Amini-Harandi, Rezapour et al., Kadelburg et al., have tried to find at least one fixed point for quasi-contractions when $alphain[frac{1}{2}, 1)$ but no clear answer exists right now and many of them either have failed or changed to a lighter version. In this paper, we introduce some new strict fixed point results in the set of multi-valued '{C}iri'{c}-generalized weak quasi-contraction mappings of integral type. We consider a necessary and sufficient condition on such mappings which guarantees the existence of unique strict fixed point of such mappings. Our result is a partial positive answer for the mentioned problem which has remained open for many years. Also, we give an strict fixed point result of $alpha$-$psi$-quasicontractive multi-valued mappings of integral type. Our results generalize and improve many existing results on multi-valued mappings in literature. Moreover, some examples are presented to support our new class of multi-valued contractions.
https://ijnaa.semnan.ac.ir/article_3511_e5747011237bd65360933a55ff42edcd.pdf
strict fixed point
'{C}iri'{c}-generalized weak quasi-contraction
multi-valued mappings
integral type
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-17
9
2
131
143
10.22075/ijnaa.2018.11892.1596
3512
An extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel
Bicheng Yang
bcyang@gdei.edu.cn
1
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China
In this paper, by the use of the weight coefficients, the transfer formula and the technique of real analysis, an extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions and a few examples are considered.
https://ijnaa.semnan.ac.ir/article_3512_74c207a1281ac51dea5d782dbbcc5f68.pdf
Hardy-Hilbert-type inequality
weight coefficient
equivalent form
operator
norm
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-17
9
2
145
159
10.22075/ijnaa.2018.12688.1647
3514
Ulam stabilities for nonlinear Volterra-Fredholm delay integrodifferential equations
Kishor Kucche
kdkucche@gmail.com
1
Pallavi Shikhare
jananishikhare13@gmail.com
2
Department of Mathematics, Shivaji University, Kolhapur-416 004, Maharashtra, India
Department of Mathematics, Shivaji University, Kolhapur-416 004, Maharashtra, India
In the present research paper we derive results about existence and uniqueness of solutions and <span>Ulam</span>--<span>Hyers</span> and <span>Rassias </span>stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of obtained results and few illustrative examples.
https://ijnaa.semnan.ac.ir/article_3514_63fd6817160ec6464f7d75a15bd85c7f.pdf
Volterra-Fredholm integrodifferential equations
Ulam-Hyers stability
Ulam-Hyers--Rassias stability
Integral inequality
Picard operator
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-18
9
2
161
167
10.22075/ijnaa.2018.3060.1495
3522
Some notes on ``Common fixed point of two $R$-weakly commuting mappings in $b$-metric spaces"
Shaoyuan Xu
xushaoyuan@126.com
1
Suyu Cheng
chengsuyu1992@126.com
2
Stojan Radenović
stojan.radenovic@tdt.edu.vn
3
School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China
Library, Hanshan Normal University, Chaozhou, 521041, China
University of Belgrade, Faculty of Mechanical Engineering, Beograd, Serbia
Very recently, Kuman et al. [P. Kumam, W. Sintunavarat, S. Sedghi, and N. Shobkolaei. Common Fixed Point of Two $R$-Weakly Commuting Mappings in $b$-Metric Spaces. Journal of Function Spaces, Volume 2015, Article ID 350840, 5 pages] obtained some interesting common fixed point results for two mappings satisfying generalized contractive condition in $b$-metric space without the assumption of the continuity of the $b$-metric, but unfortunately, there exists a gap in the proof of the main result. In this note, we point out and fill such gap by making some remarks and offering a new proof for the result. It should be mentioned that our proofs for some key assertions of the main result are new and somewhat different from the original ones. In addition, we also present a result to check the continuity of the $b$-metrics which is found effective and workable when applied to some examples.
https://ijnaa.semnan.ac.ir/article_3522_827c9ac2f28ad1c61f6bf515685d7838.pdf
$b$-metric spaces
$R$-weakly commuting mappings
the continuity concerning the $b$-metric
common fixed points
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-19
9
2
169
178
10.22075/ijnaa.2017.12355.1628
3523
Coupled fixed points of generalized Kanann contraction and its applications
Naser Ghafoori Adl
naser.ghafoori@gmail.com
1
Davood Ebrahimi Bagha
e_bagha@yahoo.com
2
Mohammad Sadegh Asgari
msasgari@yahoo.com
3
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of Mathematics Faculty of Science Islamic Azad University Central Tehran Branch
Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran
The purpose of this paper is to find of the theoretical results of fixed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized <span>Kanann</span> type <span>contractivity</span> of assumption. Also, as an application, we prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions admitting only the existence of a mixed <span>$leq$</span>-solution.
https://ijnaa.semnan.ac.ir/article_3523_0f18082d7d6d237aaa0fc831ba4718d4.pdf
Coupled fixed point
Generalized Kanann mapping
partially ordered set
Periodic boundary value problem
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-21
9
2
179
190
10.22075/ijnaa.2018.12908.1665
3524
Fixed Point Theorems For Weak Contractions in Dualistic Partial Metric Spaces
Muhammad Nazam
nazim254.butt@gmail.com
1
Arshad Muhammad
marshadzia@iiu.edu.pk
2
Department of mathematics, International Islamic University, Islamabad, Pakistan
Department of Mathematics and Statistics, International Islamic University, Islamabad Pakistan
In this paper, we describe some topological properties of <span>dualistic</span> partial metric spaces and establish some fixed point theorems for weak contraction mappings of rational type defined on dual partial metric spaces. These results are generalizations of some existing results in the literature. Moreover, we present examples to illustrate our result.
https://ijnaa.semnan.ac.ir/article_3524_2a484f1a955c18b99c48065c0b450821.pdf
fixed point
dualistic partial metric
Weak contractions
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-24
9
2
191
201
10.22075/ijnaa.2018.12972.1668
3525
On a $k$-extension of the Nielsen's $beta$-Function
Kwara Nantomah
knantomah@uds.edu.gh
1
Kottakkaran Nisar
ksnisar1@gmail.com
2
Kuldeep Gehlot
drksgehlot@rediffmail.com
3
Department of Mathematics, Faculty of Mathematical Sciences, University for Development Studies, Ghana.
Department of Mathematics, College of Arts and Science-Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Alkharj, Kingdom of Saudi Arabia
Government College Jodhpur, JNV University Jodhpur, Rajasthan, India-306401.
Motivated by the $k$-digamma function, we introduce a $k$-extension of the Nielsen's $beta$-function, and further study some properties and inequalities of the new function.
https://ijnaa.semnan.ac.ir/article_3525_262b738fee357c360fe1e5165b37d43a.pdf
Nielsen's $beta$-function
$k$-extension
$k$-digamma function
inequality
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-25
9
2
203
214
10.22075/ijnaa.2018.13630.1709
3526
Yang-Laplace transform method Volterra and Abel's integro-differential equations of fractional order
Fuat Usta
fuatusta@duzce.edu.tr
1
Huseyin Budak
hsyn.budak@gmail.com
2
Mehmet Sarikaya
sarikayamz@gmail.com
3
Department of Mathematics, Faculty of Science and Arts, D"{u}zce University, D"{u}zce, Turkey
Department of Mathematics,\ Faculty of Science and Arts, D\"{u}zce University, D\"{u}zce, Turkey
Department of Mathematics,\ Faculty of Science and Arts, D\"{u}zce University, D\"{u}zce, Turkey
This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the local fractional integral equations.
https://ijnaa.semnan.ac.ir/article_3526_33ab662aac9af5fdeb7e6becf20ed364.pdf
Local fractional calculus
Volterra and Abel’s integral equations
Yang-Laplace transform
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-26
9
2
215
221
10.22075/ijnaa.2017.1718.1640
3530
A new algorithm for computing SAGBI bases up to an arbitrary degree
Shahnaz Fakouri
sh.fakouri@std.du.ac.ir
1
Abdolali Basiri
basiri@du.ac.ir
2
Sajjad Rahmani
s_rahmani@du.ac.ir
3
Department of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
Department of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
Department of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
We present a new algorithm for computing a <span>SAGBI</span> basis up to an arbitrary degree for a <span>subalgebra</span> generated by a set of homogeneous polynomials. Our idea is based on linear algebra methods which cause a low level of complexity and computational cost. We then use it to solve the membership problem in <span>subalgebras</span>.
https://ijnaa.semnan.ac.ir/article_3530_27f14ecaa26f792a3f495500263a548b.pdf
SAGBI basis
SAGBI algorithm
subalgebra membership problem
homogeneous polynomial
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-28
9
2
223
230
10.22075/ijnaa.2018.13163.1681
3531
Certain subclass of $p$-valent meromorphic Bazilevi'{c} functions defined by fractional $q$-calculus operators
Abdul Rahman Juma
dr_juma@hotmail.com
1
Mushtaq Abdulhussain
mushtdma8@yahoo.com
2
Saba Al-khafaji
sabanf.mc11p@uokufa.edu.iq
3
University of Anbar, Department of Mathematics, Ramadi-Iraq
Department of Mathematics, Mustansiriyah University, Iraq
University of Anbar, Department of Mathematics, Ramadi-Iraq
The aim of the present paper is to introduce and investigate a new subclass of <span>Bazilevi</span><span>'</span>{c} functions in the punctured unit disk<br /> <span>$mathcal{U}^*$</span> which have been described through using of the well-known fractional <span>$q$</span>-calculus operators, Hadamard product and a linear operator. In addition, we obtain some sufficient conditions for the functions belonging to this class and for some of its subclasses.
https://ijnaa.semnan.ac.ir/article_3531_02e40a41822e83d902f511a067178334.pdf
Meromorphic $p$-valent functions
Hadamard product
Bazilevi'{c} function
fractional $q$-calculus operators
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2018-12-29
9
2
231
239
10.22075/ijnaa.2018.13447.1695
3528
A nonlinear multi objective model for the product portfolio optimization: An integer programming
Nahid Dorostkar-Ahmadi
n_dorostkar@semnan.ac.ir
1
Mohsen Shafiei Nikabadi
shafie@profs.semnan.ac.ir
2
Department of industrial management, faculty of economy, management and official science, Semnan university, Iran
Industrial Management Department Economics and Management Faculty Semnan University
Optimization of the product portfolio has been recognized as a critical problem in industry, management, economy and so on. It aims at the selection of an optimal mix of the products to offer in the target market. As a probability function, reliability is an essential objective of the problem which linear models often fail to evaluate it. Here, we develop a multiobjective integer nonlinear constraint model for the problem. Our model provides opportunities to consider the knowledge transferring cost and the environmental effects, as nowadays important concerns of the world, in addition to the classical factors operational cost and reliability. Also, the model is designed in a way to simultaneously optimize the input materials and the products. Although being to some extent complicated, the model can be efficiently solved by the metaheuristic algorithms. Finally, we make some numerical experiments on a simulated test problem.
https://ijnaa.semnan.ac.ir/article_3528_c56d3bfeaa4c68e6a9041801e356f6cf.pdf
Product portfolio optimization
nonlinear programming
multiobjective optimization
Reliability
metaheuristic algorithm