Pub Date : 2020-02-20DOI: 10.19139/soic-2310-5070-710
M. Afshari, H. Karamikabir
This paper presents shrinkage estimators of the location parameter vector for spherically symmetric distributions. We suppose that the mean vector is non-negative constraint and the components of diagonal covariance matrix is known. We compared the present estimator with natural estimator by using risk function. We show that when the covariance matrices are known, under the balance error loss function, shrinkage estimator has the smaller risk than the natural estimator. Simulation results are provided to examine the shrinkage estimators.
{"title":"The Location Parameter Estimation of Spherically Distributions with Known Covariance Matrices","authors":"M. Afshari, H. Karamikabir","doi":"10.19139/soic-2310-5070-710","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-710","url":null,"abstract":"This paper presents shrinkage estimators of the location parameter vector for spherically symmetric distributions. We suppose that the mean vector is non-negative constraint and the components of diagonal covariance matrix is known. We compared the present estimator with natural estimator by using risk function. We show that when the covariance matrices are known, under the balance error loss function, shrinkage estimator has the smaller risk than the natural estimator. Simulation results are provided to examine the shrinkage estimators.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"499-506"},"PeriodicalIF":0.0,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49330290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-18DOI: 10.19139/soic-2310-5070-705
Z. Khan, S. S. Irfan, M. F. Khan, P. Shukla
A new system of implicit n-variational inclusions is considered. We propose a new algorithm with error terms for computing the approximate solutions of our system. The convergence of the iterative sequences generated by the iterative algorithm is also discussed. Some special cases are also discussed.
{"title":"An itertive algorithm with error terms for solving a system of implicit n-variational inclusions","authors":"Z. Khan, S. S. Irfan, M. F. Khan, P. Shukla","doi":"10.19139/soic-2310-5070-705","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-705","url":null,"abstract":"A new system of implicit n-variational inclusions is considered. We propose a new algorithm with error terms for computing the approximate solutions of our system. The convergence of the iterative sequences generated by the iterative algorithm is also discussed. Some special cases are also discussed.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"242-253"},"PeriodicalIF":0.0,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48882193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-18DOI: 10.19139/soic-2310-5070-601
R. Dubey, Deepmala, V. Mishra
In this paper, we introduce the definition of higher-order K-(C,α, ρ, d)-convexity/pseudoconvexity over cone and discuss a nontrivial numerical examples for existing such type of functions. The purpose of the paper is to study higher order fractional symmetric duality over arbitrary cones for nondifferentiable Mond-Weir type programs under higherorder K -(C,α, ρ, d)-convexity/pseudoconvexity assumptions. Next, we prove appropriate duality relations under aforesaid assumptions.
{"title":"Higher-order symmetric duality in nondifferentiable multiobjective fractional programming problem over cone contraints","authors":"R. Dubey, Deepmala, V. Mishra","doi":"10.19139/soic-2310-5070-601","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-601","url":null,"abstract":"In this paper, we introduce the definition of higher-order K-(C,α, ρ, d)-convexity/pseudoconvexity over cone and discuss a nontrivial numerical examples for existing such type of functions. The purpose of the paper is to study higher order fractional symmetric duality over arbitrary cones for nondifferentiable Mond-Weir type programs under higherorder K -(C,α, ρ, d)-convexity/pseudoconvexity assumptions. Next, we prove appropriate duality relations under aforesaid assumptions.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"187-205"},"PeriodicalIF":0.0,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43759425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-18DOI: 10.19139/soic-2310-5070-382
Farid shayesteh, R. Moghaddam
Multi-objective optimization problems are so designed that they simultaneously minimize several objectives functions (which are sometimes contradictory). In most cases, the objectives are in conflict with each other such that optimization of one objective does not lead to the optimization of another ones. Therefore, we should achieve a certain balance of goals to solve these problems, which usually requires the application of an intelligent method. In this regard, use of meta-heuristic algorithms will be associated with resolved problems. In this paper, we propose a new multi-objective firefly optimization method which is designed based on the law of attraction and crowding distance. The proposed methods efficiency has been evaluated by three valid test functions containing convex, nonconvex and multi discontinuous convex Pareto fronts. Simulation results confirm the significant accuracy of proposed method in defining the Pareto front for all three test functions. In addition, the simulation results indicates that proposed algorithm has higher accuracy and greater convergence speed, compared to other well known multi-objective algorithms such as non-dominated sorting genetic algorithm, Bees algorithm, Differential Evolution algorithm and Strong Pareto Evolutionary Algorithm.
{"title":"Improving firefly-based multi-objective optimization based on attraction law and crowding distance","authors":"Farid shayesteh, R. Moghaddam","doi":"10.19139/soic-2310-5070-382","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-382","url":null,"abstract":"Multi-objective optimization problems are so designed that they simultaneously minimize several objectives functions (which are sometimes contradictory). In most cases, the objectives are in conflict with each other such that optimization of one objective does not lead to the optimization of another ones. Therefore, we should achieve a certain balance of goals to solve these problems, which usually requires the application of an intelligent method. In this regard, use of meta-heuristic algorithms will be associated with resolved problems. In this paper, we propose a new multi-objective firefly optimization method which is designed based on the law of attraction and crowding distance. The proposed methods efficiency has been evaluated by three valid test functions containing convex, nonconvex and multi discontinuous convex Pareto fronts. Simulation results confirm the significant accuracy of proposed method in defining the Pareto front for all three test functions. In addition, the simulation results indicates that proposed algorithm has higher accuracy and greater convergence speed, compared to other well known multi-objective algorithms such as non-dominated sorting genetic algorithm, Bees algorithm, Differential Evolution algorithm and Strong Pareto Evolutionary Algorithm.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"229-241"},"PeriodicalIF":0.0,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67752424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-18DOI: 10.19139/soic-2310-5070-681
Abdullah
In this paper, we introduce vector-valued nonuniform multiresolution analysis on positive half-line related to Walsh functions. We obtain the necessary and sufficient condition for the existence of associated wavelets.
{"title":"Vector-valued nonuniform multiresolution analysis related to Walsh function","authors":"Abdullah","doi":"10.19139/soic-2310-5070-681","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-681","url":null,"abstract":"In this paper, we introduce vector-valued nonuniform multiresolution analysis on positive half-line related to Walsh functions. We obtain the necessary and sufficient condition for the existence of associated wavelets.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"206-219"},"PeriodicalIF":0.0,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46470150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-18DOI: 10.19139/soic-2310-5070-690
Sergey S. Yulin, I. Palamar
The problem of recognizing patterns, when there are few training data available, is particularly relevant and arises in cases when collection of training data is expensive or essentially impossible. The work proposes a new probability model MC&CL (Markov Chain and Clusters) based on a combination of markov chain and algorithm of clustering (self-organizing map of Kohonen, k-means method), to solve a problem of classifying sequences of observations, when the amount of training dataset is low. An original experimental comparison is made between the developed model (MC&CL) and a number of the other popular models to classify sequences: HMM (Hidden Markov Model), HCRF (Hidden Conditional Random Fields),LSTM (Long Short-Term Memory), kNN+DTW (k-Nearest Neighbors algorithm + Dynamic Time Warping algorithm). A comparison is made using synthetic random sequences, generated from the hidden markov model, with noise added to training specimens. The best accuracy of classifying the suggested model is shown, as compared to those under review, when the amount of training data is low.
当可用的训练数据很少时，识别模式的问题尤其相关，并且在训练数据收集昂贵或基本上不可能的情况下会出现。本文将马尔可夫链与聚类算法（Kohonen的自组织映射，k-means方法）相结合，提出了一种新的概率模型MC&CL（Markov Chain and Clusters），以解决训练数据量较低时观测序列的分类问题。将所开发的模型（MC&CL）与其他一些流行的序列分类模型进行了初步的实验比较：HMM（隐马尔可夫模型）、HCRF（隐条件随机场）、LSTM（长短期记忆）、kNN+DTW（k-最近邻算法+动态时间Warping算法）。使用隐马尔可夫模型生成的合成随机序列进行比较，并将噪声添加到训练样本中。当训练数据量较低时，与正在审查的模型相比，显示了对所建议的模型进行分类的最佳准确性。
{"title":"Probability Model Based on Cluster Analysis to Classify Sequences of Observations for Small Training Sets","authors":"Sergey S. Yulin, I. Palamar","doi":"10.19139/soic-2310-5070-690","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-690","url":null,"abstract":"The problem of recognizing patterns, when there are few training data available, is particularly relevant and arises in cases when collection of training data is expensive or essentially impossible. The work proposes a new probability model MC&CL (Markov Chain and Clusters) based on a combination of markov chain and algorithm of clustering (self-organizing map of Kohonen, k-means method), to solve a problem of classifying sequences of observations, when the amount of training dataset is low. An original experimental comparison is made between the developed model (MC&CL) and a number of the other popular models to classify sequences: HMM (Hidden Markov Model), HCRF (Hidden Conditional Random Fields),LSTM (Long Short-Term Memory), kNN+DTW (k-Nearest Neighbors algorithm + Dynamic Time Warping algorithm). A comparison is made using synthetic random sequences, generated from the hidden markov model, with noise added to training specimens. The best accuracy of classifying the suggested model is shown, as compared to those under review, when the amount of training data is low.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"296-303"},"PeriodicalIF":0.0,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46832869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-18DOI: 10.19139/soic-2310-5070-551
H. Fazlollahtabar, M. Ashoori
This paper concerns with an integrated business process to be applied as a decision support for market analysis and decision making. The proposed business intelligence and analytics system makes use of an extract, transform and load mechanism for data collection and purification. As a mathematical decision optimization, dynamic pricing is formulated based on customer entry-exit rates in a history-based pricing model. The optimal prices for products are obtained so that aggregated profit is maximized. A case study is reported to show the effectiveness of the approach. Also, analytical investigations on the impacts of the sensitive parameters of the pricing model are given.
{"title":"Business Analytics using Dynamic Pricing based on Customer Entry-Exit Rates Tradeoff","authors":"H. Fazlollahtabar, M. Ashoori","doi":"10.19139/soic-2310-5070-551","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-551","url":null,"abstract":"This paper concerns with an integrated business process to be applied as a decision support for market analysis and decision making. The proposed business intelligence and analytics system makes use of an extract, transform and load mechanism for data collection and purification. As a mathematical decision optimization, dynamic pricing is formulated based on customer entry-exit rates in a history-based pricing model. The optimal prices for products are obtained so that aggregated profit is maximized. A case study is reported to show the effectiveness of the approach. Also, analytical investigations on the impacts of the sensitive parameters of the pricing model are given.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"272-280"},"PeriodicalIF":0.0,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45136062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-18DOI: 10.19139/soic-2310-5070-532
A. Halilu, M. Waziri, Y. B. Musa
In this paper, a single direction with double step length method for solving systems of nonlinear equations is presented. Main idea used in the algorithm is to approximate the Jacobian via acceleration parameter. Furthermore, the two step lengths are calculated using inexact line search procedure. This method is matrix-free, and so is advantageous when solving large-scale problems. The proposed method is proven to be globally convergent under appropriate conditions. The preliminary numerical results reported in this paper using a large-scale benchmark test problems show that the proposed method is practically quite effective.
{"title":"Inexact Double Step Length Method For Solving Systems Of Nonlinear Equations","authors":"A. Halilu, M. Waziri, Y. B. Musa","doi":"10.19139/soic-2310-5070-532","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-532","url":null,"abstract":"In this paper, a single direction with double step length method for solving systems of nonlinear equations is presented. Main idea used in the algorithm is to approximate the Jacobian via acceleration parameter. Furthermore, the two step lengths are calculated using inexact line search procedure. This method is matrix-free, and so is advantageous when solving large-scale problems. The proposed method is proven to be globally convergent under appropriate conditions. The preliminary numerical results reported in this paper using a large-scale benchmark test problems show that the proposed method is practically quite effective.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"165-174"},"PeriodicalIF":0.0,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48659149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-18DOI: 10.19139/soic-2310-5070-741
M. Aliane, N. Moussouni, Mohand Bentobache
In this work, we have modelled the problem of maximizing the velocity of a rocket moving with a rectilinear motion by a linear optimal control problem, where the control represents the action of the pilot on the rocket. In order to solve the obtained model, we applied both analytical and numerical methods. The analytical solution is calculated using the Pontryagin maximum principle while the approximate solution of the problem is found using the shooting method as well as two techniques of discretization: the technique using the Cauchy formula and the one using the Euler formula. In order to compare the different methods, we developed an implementation with MATLAB and presented some simulation results.
{"title":"Optimal control of a rectilinear motion of a rocket","authors":"M. Aliane, N. Moussouni, Mohand Bentobache","doi":"10.19139/soic-2310-5070-741","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-741","url":null,"abstract":"In this work, we have modelled the problem of maximizing the velocity of a rocket moving with a rectilinear motion by a linear optimal control problem, where the control represents the action of the pilot on the rocket. In order to solve the obtained model, we applied both analytical and numerical methods. The analytical solution is calculated using the Pontryagin maximum principle while the approximate solution of the problem is found using the shooting method as well as two techniques of discretization: the technique using the Cauchy formula and the one using the Euler formula. In order to compare the different methods, we developed an implementation with MATLAB and presented some simulation results.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"281-295"},"PeriodicalIF":0.0,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45425686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-18DOI: 10.19139/soic-2310-5070-621
N. Sweilam, S. Al-Mekhlafi, A. O. Albalawi
In this paper, a novel mathematical distributed order fractional model of multi-strain Tuberculosis is presented. The proposed model is governed by a system of distributed order fractional differential equations, where the distributed order fractional derivative is defined in the sense of the Grünwald−Letinkov definition. A nonstandard finite difference method is proposed to study the resulting system . The stability analysis of the proposed model is discussed. Numerical simulations show that, the nonstandard finite difference method can be applied to solve such distributed order fractional differential equations simply and effectively.
{"title":"On the Distributed Order Fractional Multi-Strain Tuberculosis Model: a Numerical Study","authors":"N. Sweilam, S. Al-Mekhlafi, A. O. Albalawi","doi":"10.19139/soic-2310-5070-621","DOIUrl":"https://doi.org/10.19139/soic-2310-5070-621","url":null,"abstract":"In this paper, a novel mathematical distributed order fractional model of multi-strain Tuberculosis is presented. The proposed model is governed by a system of distributed order fractional differential equations, where the distributed order fractional derivative is defined in the sense of the Grünwald−Letinkov definition. A nonstandard finite difference method is proposed to study the resulting system . The stability analysis of the proposed model is discussed. Numerical simulations show that, the nonstandard finite difference method can be applied to solve such distributed order fractional differential equations simply and effectively.","PeriodicalId":93376,"journal":{"name":"Statistics, optimization & information computing","volume":"8 1","pages":"175-186"},"PeriodicalIF":0.0,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48282396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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