Control and Optimization
Akbar Hashemi Borzabadi; Manije Hasanabadi; Navid Sadjadi
Volume 1, Issue 1 , April 2016, , Pages 1-19
Abstract
In this paper an approach based on evolutionary algorithms to find Pareto optimal pair of state and control for multi-objective optimal control problems (MOOCP)'s is introduced. In this approach, first a discretized form of the time-control space is considered and then, a ...
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In this paper an approach based on evolutionary algorithms to find Pareto optimal pair of state and control for multi-objective optimal control problems (MOOCP)'s is introduced. In this approach, first a discretized form of the time-control space is considered and then, a piecewise linear control and a piecewise linear trajectory are obtained from the discretized time-control space using a numerical method. To do that, a modified version of two famous evolutionary genetic algorithm (GA) and particle swarm optimization (PSO) to obtain Pareto optimal solutions of the problem is employed. Numerical examples are presented to show the efficiency of the given approach.
Control and Optimization
Hassan Zarei
Volume 1, Issue 2 , October 2016, , Pages 1-21
Abstract
In this paper, a computational approach is adopted for solving a multi-objective optimal control problem (MOOCP) formulation of optimal drug scheduling in human immunodeficiency (HIV) virus infected by individuals. The MOOCP, which uses a mathematical model of HIV infection, ...
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In this paper, a computational approach is adopted for solving a multi-objective optimal control problem (MOOCP) formulation of optimal drug scheduling in human immunodeficiency (HIV) virus infected by individuals. The MOOCP, which uses a mathematical model of HIV infection, has some incompatible objectives. The objectives are maximizing the survival time of patients, the level of D4+ T-cells and the level of cytotoxic T-lymphocytes (CTLs), and minimizing the viral load and the drug costs. In this approach the fuzzy goals described by the linear membership functions, are incorporated for the objectives and the optimal solution is investigated by maximizing the degree of attainment of the aggregated fuzzy goals resulting a fuzzy goal optimal control problem (FGOCP). Using the minimum operator for aggregation of fuzzy goals, the FGOCP is converted into a constrained optimal control problem (OCP) in canonical form. The control parametrization enhancing technique (CPET) is used for approximating the OCP by an optimal parameter selection problem, with the final goal of implementing continuous and interrupted (structured treatment interruptions, STI) combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficacies. Efficiency of the proposed method is confirmed by numerical simulations.
Control and Optimization
Zahra Rafiei; Behzad Kafash; Seyyed Mehdi Karbassi
Volume 2, Issue 1 , April 2017, , Pages 1-13
Abstract
In order to obtain a solution to an optimal control problem, a numerical technique based on state-control parameterization method is presented. This method can be facilitated by the computation of performance index and state equation via approximating the control and state variable ...
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In order to obtain a solution to an optimal control problem, a numerical technique based on state-control parameterization method is presented. This method can be facilitated by the computation of performance index and state equation via approximating the control and state variable as a function of time. Several numerical examples are presented to confirm the analytical findings and illustrate the efficiency of the proposed method.
Control and Optimization
Saeed Nezhadhosein
Volume 2, Issue 2 , December 2017, , Pages 1-14
Abstract
In this paper, Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems. Firstly, using necessary conditions for optimality, the problem is changed into a two-boundary value problem (TBVP). Next, ...
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In this paper, Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems. Firstly, using necessary conditions for optimality, the problem is changed into a two-boundary value problem (TBVP). Next, Haar wavelets are applied for converting the TBVP, as a system of differential equations, in to a system of matrix algebraic equations, as Haar matrix equations using Kronecker product. Then the error analysis of the proposed method is presented. Some numerical examples are given to demonstrate the efficiency of the method. The solutions converge as the number of approximate terms increase.
Control and Optimization
seyed mehdy shafiof; Javad Askari; Maryam Shams Solary
Abstract
In this paper, a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly. First, the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs). Then, ...
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In this paper, a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly. First, the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs). Then, the unknown functions are approximated by the hybrid functions, including Bernoulli polynomials and Block-pulse functions based on the spectral Ritz method. Also, two new methods are proposed for calculating the left Caputo fractional derivative and right Riemann-Liouville fractional derivative operators of the hybrid functions that are proportional to the Ritz method. The FOCP is converted into a system of the algebraic equations by applying the fractional derivative operators and collocation method, which determines the solution of the problem. Error estimates for the hybrid function approximation, fractional operators and, the proposed method are provided. Finally, the efficiency of the proposed method and its accuracy in obtaining optimal solutions are shown by some test problems.
Atefeh Hassani Bafrani; Ali Sadeghieh
Abstract
In 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 ...
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In 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.
Ali Reza Shojaeifard; Hamid Reza Yazdani; Mohsen Shahrezaee
Abstract
In this paper, we are going to analyze big data (embedded in the digital images) with new methods of tensor completion (TC). The determination of tensor ranks and the type of decomposition are significant and essential matters. For defeating these problems, Bayesian ...
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In this paper, we are going to analyze big data (embedded in the digital images) with new methods of tensor completion (TC). The determination of tensor ranks and the type of decomposition are significant and essential matters. For defeating these problems, Bayesian CP-Factorization (BCPF) is applied to the tensor completion problem. The \textit{BCPF} can optimize the type of ranks and decomposition for achieving the best results. In this paper, the hybrid method is proposed by integrating BCPF and general TC. The tensor completion problem was briefly introduced. Then, based on our implementations, and related sources, the proposed tensor-based completion methods emphasize their strengths and weaknesses. Theoretical, practical, and applied theories have been discussed and two of them for analyzing big data have been selected, and applied to several examples of selected images. The results are extracted and compared to determine the method's efficiency and importance compared to each other. Finally, the future ways and the field of future activity are also presented.
Majid Roohi; Mohammad Pourmahmood Aghababa; Javid Ziaei; Chongqi Zhang
Abstract
The present study introduces a kind of fractional-order Hopfield neural network (FOHNN), and its complex dynamic behavior is investigated through chaos analyses. With the use of phase space analysis and bifurcation diagrams and maximal Lyapunov exponent (MLE) it is demonstrated that ...
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The present study introduces a kind of fractional-order Hopfield neural network (FOHNN), and its complex dynamic behavior is investigated through chaos analyses. With the use of phase space analysis and bifurcation diagrams and maximal Lyapunov exponent (MLE) it is demonstrated that for the values of 0.87 < α < 1, as the fractional-order (FO), the dynamical behavior of the mentioned FOHNN is chaotic. Then, the bounded trait of chaotic systems is utilized to derive an adaptive model-free control technique to suppress of complex dynamics of the FOHNN. Furthermore, according to the matrix analysis theorem of non-integer-order systems and the adaptive model-free control methodology, analytical consequences of the designed controller are evidenced. Eventually, two examples are reported to illustrate the applicability of the mentioned model-free control method.
Sayyed Hossein Ejtahed; Naser Pariz; Ali Karimpour
Abstract
Switched linear systems are noted as a major category of control systems. Fault detection of these systems is affected by switching phenomena and therefore their integrated fault detection and robust control (IFDRC) are the central issues of recent studies. Existing studies on IFDRC ...
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Switched linear systems are noted as a major category of control systems. Fault detection of these systems is affected by switching phenomena and therefore their integrated fault detection and robust control (IFDRC) are the central issues of recent studies. Existing studies on IFDRC do not consider the effects of all of the parameter uncertainties, input disturbance, and mode-dependent time-varying state delay in the presence of mode-dependent average dwell time (MDADT) switching together in these systems. To address the issue based on output feedback, in this paper, the IFDRC design problem is formulated as a multi-objective or mixed H∞/H- optimization problem. H∞ performance indicator guarantees the robustness of residual to disturbance, and H- performance represents the sensitivity index of residual to the fault. A piecewise Lyapunov-Krasovskii function is employed together with the MDADT scheme and therefore, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) in order to deal with the problem. Then to clarify the design procedure, we also present an algorithm in the light of the proposed approach. Eventually, to illustrate the efficiency of the suggested approach, the designed IFDRC framework is simulated for a case study of an Electrical Circuit system.
Mohammad Reza Zarrabi
Abstract
Drones are among the most valuable and versatile technologies in the world, with applications in a vast number of fields such as traffic control, agriculture, firefighting and rescue, and filmmaking, to name a few. As ...
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Drones are among the most valuable and versatile technologies in the world, with applications in a vast number of fields such as traffic control, agriculture, firefighting and rescue, and filmmaking, to name a few. As the development of unmanned aerial vehicles (UAVs) accelerates, the safety of UAVs becomes increasingly important. In this paper, a robust adaptive controller is designed to improve the safety of a hexa-rotor UAV, and a robust adaptive controller is developed to control our system. In doing so, the wind parameters from the aerodynamic forces and moments acting on the hexa-rotor are estimated using an observer with the adaptive algorithm. This proposed controller guarantees stability and reliable function in the midst of parametric and non-parametric uncertainties. The process's global stability and tracking convergence are investigated using the Lyapunov theorem. The performance and effectiveness of the proposed controller are tested through two simulation studies, which take into account external disturbances that are a function of time.
Saeed Nezhadhosein; Reza Ghanbari; Khatere Ghorbani-Moghadam
Abstract
In this paper, we solve a class of nonlinear optimal control problems using a hybrid genetic algorithm (HGA) and a direct method based on the Haar wavelets where the performance index is Bolza-form and the dynamic system is linear. First, we change the problem by using HWs to a static ...
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In this paper, we solve a class of nonlinear optimal control problems using a hybrid genetic algorithm (HGA) and a direct method based on the Haar wavelets where the performance index is Bolza-form and the dynamic system is linear. First, we change the problem by using HWs to a static optimization problem in which the decision variables are the unknown coefficients of the state and control variables in the Haar series. Next, we apply HGA with a local search for higher power of GA in investigating the search space for solving optimization problems. Finally, we give some examples to illustrate the high accuracy of the proposed method.
Mahmood Amintoosi; Eisa Kohan-Baghkheirati
Abstract
Every year, extensive experimental analysis is conducted to evaluate the anti-cancer properties of plants. Developing a well-ranked list of potential anti-cancer plants based on verified anti-cancer metabolites can significantly reduce the time and cost required for plant evaluation. ...
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Every year, extensive experimental analysis is conducted to evaluate the anti-cancer properties of plants. Developing a well-ranked list of potential anti-cancer plants based on verified anti-cancer metabolites can significantly reduce the time and cost required for plant evaluation. This paper proposes a method for generating such a ranked list by analyzing biological graphs of plant-metabolite interactions. In this approach, graph nodes are ranked based on specific graph features. However, a challenge arises in selecting the most informative graph features that ensure the resulting ranked plant list is more relevant, prioritizing plants with greater anti-cancer properties at the top. To address this challenge, we propose the use of the Average Precision metric commonly used in information retrieval and recommender systems, to compare different ranked lists. By constructing a network that captures the similarities between plants based on their shared metabolites, and ranking plants using different combinations of graph features, we can identify the subset of features that yields a ranked list with a higher Average Precision score. This subset of features can then be considered the most suitable for recommending anti-cancer plants. The proposed method can be used to select the best graph features for screening unverified plant lists for anti-cancer properties, increasing the likelihood of identifying plants with higher scores in the list that possess anti-cancer properties.
Mostafa Boroumandzadeh; Elham Parvinnia; Reza Boostani; Sepideh Sefidbakht
Abstract
Medical decision support systems (MDSS) are designed to assist physicians in making accurate decisions. The required data by MDSS are collected from various resources such as physical examinations and electronic health records (EHR). In this paper, an MDSS framework has ...
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Medical decision support systems (MDSS) are designed to assist physicians in making accurate decisions. The required data by MDSS are collected from various resources such as physical examinations and electronic health records (EHR). In this paper, an MDSS framework has been proposed to diagnose and classify breast cancer patients (DSS-BC). Medical texts reports (MTR) were embedded, and essential feature vectors combined with EHR were extracted using principal component analysis (PCA). A new method based on a fuzzy min-max neural network with hyper box variable expansion coefficient (FMNN-HVEC) was used to determine the molecular subtypes, and the feature vectors were clustered using deep clustering. Also, a new decision fusion algorithm called weighted Yager was proposed based on the F1-Score for each class. This algorithm proposed a mathematical decision fusion technique to determine the Breast Imaging-Reporting and Data System (BI-RADS) and molecular subtypes values with the accuracy of 95.12% and 89.56%, respectively.
Ahmad Rezayi
Abstract
For 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, ...
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For 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.
Control and Optimization
Hadi Nasseri; Davood Darvishi Salokolaei; Allahbakhsh Yazdani
Volume 2, Issue 1 , April 2017, , Pages 15-28
Abstract
Linear assignment problem is one of the most important practical models in the literature of linear programming problems. Input data in the cost matrix of the linear assignment problem are not always crisp and sometimes in the practical situations is formulated by the grey systems theory approach. ...
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Linear assignment problem is one of the most important practical models in the literature of linear programming problems. Input data in the cost matrix of the linear assignment problem are not always crisp and sometimes in the practical situations is formulated by the grey systems theory approach. In this way, some researchers have used a whitening technique to solve the grey assignment problem. Since the whitening technique only provides a crisp equivalent model and does not reflect the evolutionary characteristics of a grey set, it cannot keep the uncertainty properties in an interval involving the optimal solution. Based on these shortcomings, in this paper a new direct approach is introduced to solve linear assignment problem in grey environments. For preparing the mentioned method, some theoretical results are given to support the methodology. Finally, a numerical example will be solved to test the validity of the proposed method. Based on the suggested methodology, we emphasize that the same approach can be used whenever any linear programming model is formulated in grey environments.
Control and Optimization
Davood Darvishi Salookolaei; Sifeng Liu; Parvin Babaei
Volume 2, Issue 2 , December 2017, , Pages 15-32
Abstract
Considering the fact that Iran is situated in an arid and semi-arid region, rainfall prediction for the management of water resources is very important and necessary. Researchers have proposed various prediction methods that have been utilized in such areas as water and meteorology, especially water ...
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Considering the fact that Iran is situated in an arid and semi-arid region, rainfall prediction for the management of water resources is very important and necessary. Researchers have proposed various prediction methods that have been utilized in such areas as water and meteorology, especially water resources management. The present study aimed at predicting rainfall amounts using Grey Prediction Method. It is a novel approach in confrontation with uncertainties in the aquiferous region of Babolrud to serve for the water resources management purposes. Therefore, expressing the concepts of Grey Prediction Methods using the collected data, at a 12-year timeframe of 2006 and 2017, rainfall prediction in 2018 and 2022 were also implemented with three methods GM(1,1), DGM(2,1) and Verhulest models. According to the calculated error and the predictive power, GM(1,1) method is better than other models and was placed within the set of good predictions. Also, we predict that in 2027, there might be a drought. According to the small samples and calculations required in this approach, the method is suggested for rainfall prediction in inexact environments. The authors can use fuzzy grey systems to predict the amount of rainfall in uncertaint environments.
Zahra Noori; Hamed Zhiani Rezai; Alireza Davoodi; Sohrab Kordrostami
Abstract
Data envelopment analysis models are able to rank decision-making units (DMUs) based on their efficiency scores. In spite of the fact that there exists a unique ranking of inefficient DMUs, ranking efficient DMUs is problematic. However, rather than ranking methods, ...
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Data envelopment analysis models are able to rank decision-making units (DMUs) based on their efficiency scores. In spite of the fact that there exists a unique ranking of inefficient DMUs, ranking efficient DMUs is problematic. However, rather than ranking methods, another way to choose one of the efficient units is to determine the most efficient DMU. Up to the present, many models have been proposed to rank DMUs and determine the most efficient one. These models require solving nonlinear or integer programs, which are NP-hard and time-consuming. Considering efficient DMU's characteristics, this paper proposes a procedure to find the most efficient DMU through some simple operations. The validity of the proposed approach is verified and tested via some numerical examples.
Rasoul Heydari Dastjerdi; Ghasem Ahmadi; Mahmood Dadkhah; Ayatollah Yari
Abstract
This paper presents a novel approach using artificial neural networks to solve the SEIR (Susceptible, Exposed, Infected, and Recovered) model of infectious diseases based on dynamical systems. Optimal control techniques are employed to determine a vaccination schedule ...
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This paper presents a novel approach using artificial neural networks to solve the SEIR (Susceptible, Exposed, Infected, and Recovered) model of infectious diseases based on dynamical systems. Optimal control techniques are employed to determine a vaccination schedule for a standard SEIR epidemic model. The multilayer perceptron is utilized to approximate the state and co-state functions of the SEIR model and to solve the optimal control problem by utilizing a nonlinear programming approach. By constructing a loss function and using Pontryagin's Minimum Principle (PMP) for the SEIR model, a minimization problem is defined, a minimization problem is defined, and the approximate solution of the Hamiltonian system is computed. This method is compared with the fourth-order Runge-Kutta method. The proposed approach's effectiveness is demonstrated through illustrative examples.
Zeinab Saeidian; Maryam Mahmoudoghli
Abstract
The Proximal Stochastic Average Gradient (Prox-SAG+) is a primary method used for solving optimization problems that contain the sum of two convex functions. This kind of problem usually arises in machine learning, which utilizes a large amount of data to create component functions from a dataset. ...
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The Proximal Stochastic Average Gradient (Prox-SAG+) is a primary method used for solving optimization problems that contain the sum of two convex functions. This kind of problem usually arises in machine learning, which utilizes a large amount of data to create component functions from a dataset. A proximal operation is applied to obtain the optimal value due to its appropriate properties. The Prox-SAG+ algorithm is faster than some other methods and has a simpler algorithm than previous ones. Moreover, using this specific operator can help to reassure that the achieved result is optimal. Additionally, it has been proven that the proposed method has an approximately geometric rate of convergence. Implementing the proposed operator makes the method more practical than other algorithms found in the literature. Numerical analysis also confirms the efficiency of the proposed scheme.
Control and Optimization
Nader Kanzi
Volume 1, Issue 1 , April 2016, , Pages 21-30
Abstract
In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are locally Lipschitz. Necessary optimality conditions and regularity conditions are given. Our approach are based on the ...
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In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are locally Lipschitz. Necessary optimality conditions and regularity conditions are given. Our approach are based on the Michel-Penot subdifferential.
Control and Optimization
Ali Nehrani; Mohammad Keyanpour
Volume 1, Issue 2 , October 2016, , Pages 23-38
Abstract
In the present paper, optimal heating of temperature field which is modelled as a boundary optimal control problem, is investigated in the uncertain environments and then it is solved numerically. In physical modelling, a partial differential equation with ...
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In the present paper, optimal heating of temperature field which is modelled as a boundary optimal control problem, is investigated in the uncertain environments and then it is solved numerically. In physical modelling, a partial differential equation with stochastic input and stochastic parameter are applied as the constraint of the optimal control problem. Controls are implemented as Dirichlet boundary conditions and representing the heating elements on the boundary of the field. In numerical quantification, stochastic input and parameter are approximated via Karhunen-Lo\'eve expansion and inserted to the problem. In fact, for numerical discretization of the problem stochastic Galerkin method is applied to generalize polynomial chaos. Numerical optimization is performed via gradient method. The problem is fully implemented and in order to show the applicability of the method, numerical examples are solved and numerical results are represented through figures.
Fatemeh Gorgini Shabankareh; Nader Kanzi; Javad Izadi; Kamal Fallahi
Abstract
In this paper, some constraint qualifications of the Guignard type are defined for optimization problems with continuously differentiable objective functions and locally Lipschitz switching constraints. Then, a new type of stationary condition, named ...
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In this paper, some constraint qualifications of the Guignard type are defined for optimization problems with continuously differentiable objective functions and locally Lipschitz switching constraints. Then, a new type of stationary condition, named parametric stationary condition, is presented for the problem, and it is shown that all the stationarity conditions in various papers can be deduced from it. This paper can be considered as an extension of a recent article (see Kanzow, et al.) to the nonsmooth case. Finally, the article ends with two important examples. The results of the article are formulated according to Clark subdifferential and using nonsmooth analysis methods.
Control and Optimization
Farzad Rahpeymaii; majid rostami
Abstract
In this paper, two extended three-term conjugate gradient methods based on the Liu-Storey ({\tt LS}) conjugate gradient method are presented to solve unconstrained optimization problems. A remarkable property of the proposed methods is that the search direction always satisfies ...
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In this paper, two extended three-term conjugate gradient methods based on the Liu-Storey ({\tt LS}) conjugate gradient method are presented to solve unconstrained optimization problems. A remarkable property of the proposed methods is that the search direction always satisfies the sufficient descent condition independent of line search method, based on eigenvalue analysis. The global convergence of proposed algorithms is established under suitable conditions. Preliminary numerical results show that the proposed methods are efficient and robust to solve the unconstrained optimization problems.
Kobra Mohammadsalahi; Farzin Modarres Khiyabani; Nima Azarmir Shotorbani
Abstract
This paper presents a capable recurrent neural network, the so-called µRNN for solving a class of non-convex quadratic programming problems. Based on the optimality conditions we construct a new recurrent neural network (µRNN), which has a simple structure and its capability ...
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This paper presents a capable recurrent neural network, the so-called µRNN for solving a class of non-convex quadratic programming problems. Based on the optimality conditions we construct a new recurrent neural network (µRNN), which has a simple structure and its capability is preserved. The proposed neural network model is stable in the sense of Lyapunov and converges to the exact optimal solution of the original problem. In a particular case, the optimality conditions of the problem become necessary and sufficient. Numerical experiments and comparisons with some existing algorithms are presented to illustrate the theoretical results and show the efficiency of the proposed network.
Farhad Hadinejad; Saeed Kazem
Abstract
In 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 ...
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In 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.