With the applications of big data, the research of real-time pricing method for smart grid has become increasingly important. Based on the demand side management and the real-time pricing model, the social welfare maximization model of smart grid is considered. We transform it by Karush-Kuhn-Tucker condition, then the social welfare maximization model is transformed into a nonsmooth equation by Fischer-Burmeister function. Then, taking advantage of simple calculation and small storage, we propose a new smoothing conjugate gradient method to solve real-time pricing problem for smart grid based on the social welfare maximization. Under general conditions, the global convergence of the new proposed method is proved. Finally, the numerical simulation results show the effectiveness of the proposed method for solving the real-time pricing problems for smart grid based on the social welfare maximization.
{"title":"Real-time pricing method for smart grid based on social welfare maximization model","authors":"Yanxue Yang, Shouhong Du, Yuan-yuan Chen","doi":"10.3934/jimo.2022039","DOIUrl":"https://doi.org/10.3934/jimo.2022039","url":null,"abstract":"With the applications of big data, the research of real-time pricing method for smart grid has become increasingly important. Based on the demand side management and the real-time pricing model, the social welfare maximization model of smart grid is considered. We transform it by Karush-Kuhn-Tucker condition, then the social welfare maximization model is transformed into a nonsmooth equation by Fischer-Burmeister function. Then, taking advantage of simple calculation and small storage, we propose a new smoothing conjugate gradient method to solve real-time pricing problem for smart grid based on the social welfare maximization. Under general conditions, the global convergence of the new proposed method is proved. Finally, the numerical simulation results show the effectiveness of the proposed method for solving the real-time pricing problems for smart grid based on the social welfare maximization.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134320012","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}
The importance of knowledge and technology is self-evident, especially the core technology of key nodes in the industrial chain, which will change the country's status in the supply chain, and even the national economic security. This scenario has led to a global non-cooperative innovation competition. In order to ensure the safety of local industrial chain and shorten the technological distance with developed countries, emerging economies can adopt imitative innovation by observing the core technologies from developed countries, or choose independent innovation strategy. How should emerging economies make the choice? We analyze this problem by establishing a dynamic non-cooperative technology development model. The research results show that when the innovation capacity gap between emerging economies and developed regions is large, the choice of imitation strategy is highly necessary. And when the gap is small, the independent innovation strategy can be selected. In addition, due to the existence of both domestic and foreign markets, developed countries can adopt strict policies to restrict the sale of products containing core technologies to overseas markets to limit the spillover of important technologies. We also consider the impact of policies that limit technology spillovers and show the impact of local market capacity in emerging economies.
{"title":"Imitative innovation or independent innovation strategic choice of emerging economies in non-cooperative innovation competition","authors":"Yang Liu, Zhiying Liu, Kaifei Xu","doi":"10.3934/jimo.2022023","DOIUrl":"https://doi.org/10.3934/jimo.2022023","url":null,"abstract":"The importance of knowledge and technology is self-evident, especially the core technology of key nodes in the industrial chain, which will change the country's status in the supply chain, and even the national economic security. This scenario has led to a global non-cooperative innovation competition. In order to ensure the safety of local industrial chain and shorten the technological distance with developed countries, emerging economies can adopt imitative innovation by observing the core technologies from developed countries, or choose independent innovation strategy. How should emerging economies make the choice? We analyze this problem by establishing a dynamic non-cooperative technology development model. The research results show that when the innovation capacity gap between emerging economies and developed regions is large, the choice of imitation strategy is highly necessary. And when the gap is small, the independent innovation strategy can be selected. In addition, due to the existence of both domestic and foreign markets, developed countries can adopt strict policies to restrict the sale of products containing core technologies to overseas markets to limit the spillover of important technologies. We also consider the impact of policies that limit technology spillovers and show the impact of local market capacity in emerging economies.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"490 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115605123","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}
Xiaoxi Zhu, Kai Liu, Miaomiao Wang, Rui Zhang, Minglun Ren
With the enhancement of environmental protection, more and more enterprises begin to develop green products. However, the high cost of green R&D leads to an increase of product price, which reduces the competitiveness of green products. In this paper, we model a supply chain which consists of one manufacturer and one retailer providing a primary product and a substitutable green added product in the market. In order to capture the impact of consumer behavior on the supply chain members' decision-making, we classify the market into two segments and assume that high-end green consumers have higher preferences for green products than ordinary consumers. Different to existing research, we assume ordinary consumers hold a positive but lower green preference compared to the green consumers. When analyzing the impacts of consumers' green preferences, we find that there exist specific boundaries of cost and market potential which define the optimal pricing strategy and product line design. Regarding profits, we find that when the green preferences of high-end and low-end consumers increase in the same proportion, the high-end market may not bring greater supply chain revenue. In particular, the marginal profit increase of the manufacturer is always greater than that of the retailer.
{"title":"Product line extension with a green added product: Impacts of segmented consumer preference on supply chain improvement and consumer surplus","authors":"Xiaoxi Zhu, Kai Liu, Miaomiao Wang, Rui Zhang, Minglun Ren","doi":"10.3934/jimo.2022021","DOIUrl":"https://doi.org/10.3934/jimo.2022021","url":null,"abstract":"With the enhancement of environmental protection, more and more enterprises begin to develop green products. However, the high cost of green R&D leads to an increase of product price, which reduces the competitiveness of green products. In this paper, we model a supply chain which consists of one manufacturer and one retailer providing a primary product and a substitutable green added product in the market. In order to capture the impact of consumer behavior on the supply chain members' decision-making, we classify the market into two segments and assume that high-end green consumers have higher preferences for green products than ordinary consumers. Different to existing research, we assume ordinary consumers hold a positive but lower green preference compared to the green consumers. When analyzing the impacts of consumers' green preferences, we find that there exist specific boundaries of cost and market potential which define the optimal pricing strategy and product line design. Regarding profits, we find that when the green preferences of high-end and low-end consumers increase in the same proportion, the high-end market may not bring greater supply chain revenue. In particular, the marginal profit increase of the manufacturer is always greater than that of the retailer.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114268510","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}
This paper studies ruin probabilities of a generalized bidimensional risk model with dependent and heavy-tailed claims and additional net loss processes. When the claim sizes have long-tailed and dominated-varying-tailed distributions, precise asymptotic formulae for two kinds of finite-time ruin probabilities are derived, where the two claim-number processes from different lines of business are almost arbitrarily dependent. Under some extra conditions on the independence relation of claim inter-arrival times, the class of the claim-size distributions is extended to the subexponential distribution class. In order to verify the accuracy of the obtained theoretical result, a simulation study is performed via the crude Monte Carlo method.
{"title":"Asymptotic estimates for finite-time ruin probabilities in a generalized dependent bidimensional risk model with CMC simulations","authors":"Xinru Ji, Bingjie Wang, Jigao Yan, Dongya Cheng","doi":"10.3934/jimo.2022036","DOIUrl":"https://doi.org/10.3934/jimo.2022036","url":null,"abstract":"This paper studies ruin probabilities of a generalized bidimensional risk model with dependent and heavy-tailed claims and additional net loss processes. When the claim sizes have long-tailed and dominated-varying-tailed distributions, precise asymptotic formulae for two kinds of finite-time ruin probabilities are derived, where the two claim-number processes from different lines of business are almost arbitrarily dependent. Under some extra conditions on the independence relation of claim inter-arrival times, the class of the claim-size distributions is extended to the subexponential distribution class. In order to verify the accuracy of the obtained theoretical result, a simulation study is performed via the crude Monte Carlo method.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130828163","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}
In this paper, we consider two common scalarization functions and their applications via asymptotic analysis. We mainly analyze the recession and asymptotic properties of translation invariant function and oriented distance function, and discuss their monotonicity and Lipschitz continuity in terms of recession functions. Finally, we apply these scalarization functions to the characterization of the nonemptiness and boundedness of the solution set for a general constrained nonconvex optimization problem.
{"title":"Asymptotic analysis of scalarization functions and applications","authors":"Genghua Li, Shengjie Li, M. You","doi":"10.3934/jimo.2022046","DOIUrl":"https://doi.org/10.3934/jimo.2022046","url":null,"abstract":"In this paper, we consider two common scalarization functions and their applications via asymptotic analysis. We mainly analyze the recession and asymptotic properties of translation invariant function and oriented distance function, and discuss their monotonicity and Lipschitz continuity in terms of recession functions. Finally, we apply these scalarization functions to the characterization of the nonemptiness and boundedness of the solution set for a general constrained nonconvex optimization problem.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114064865","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}
In this paper, we prove that the tensor complementarity problem with the begin{document}$ P_0 $end{document} mapping on the begin{document}$ n $end{document}-dimensional nonnegative orthant is solvable and the solution set is nonempty and compact under mild assumptions. Since the involved homogeneous polynomial is a begin{document}$ P_0 $end{document} mapping on the begin{document}$ n $end{document}-dimensional nonnegative orthant, the existing smoothing Newton methods are not directly used to solve this problem. So, we propose a smoothing Newton method preserving nonnegativity via a new one-dimensional line search rule for solving such problem. The global convergence is established and preliminary numerical results illustrate that the proposed algorithm is efficient and very promising.
In this paper, we prove that the tensor complementarity problem with the begin{document}$ P_0 $end{document} mapping on the begin{document}$ n $end{document}-dimensional nonnegative orthant is solvable and the solution set is nonempty and compact under mild assumptions. Since the involved homogeneous polynomial is a begin{document}$ P_0 $end{document} mapping on the begin{document}$ n $end{document}-dimensional nonnegative orthant, the existing smoothing Newton methods are not directly used to solve this problem. So, we propose a smoothing Newton method preserving nonnegativity via a new one-dimensional line search rule for solving such problem. The global convergence is established and preliminary numerical results illustrate that the proposed algorithm is efficient and very promising.
{"title":"A smoothing Newton method preserving nonnegativity for solving tensor complementarity problems with $ P_0 $ mappings","authors":"Yan Li, Lu Zhang","doi":"10.3934/jimo.2022041","DOIUrl":"https://doi.org/10.3934/jimo.2022041","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we prove that the tensor complementarity problem with the <inline-formula><tex-math id=\"M2\">begin{document}$ P_0 $end{document}</tex-math></inline-formula> mapping on the <inline-formula><tex-math id=\"M3\">begin{document}$ n $end{document}</tex-math></inline-formula>-dimensional nonnegative orthant is solvable and the solution set is nonempty and compact under mild assumptions. Since the involved homogeneous polynomial is a <inline-formula><tex-math id=\"M4\">begin{document}$ P_0 $end{document}</tex-math></inline-formula> mapping on the <inline-formula><tex-math id=\"M5\">begin{document}$ n $end{document}</tex-math></inline-formula>-dimensional nonnegative orthant, the existing smoothing Newton methods are not directly used to solve this problem. So, we propose a smoothing Newton method preserving nonnegativity via a new one-dimensional line search rule for solving such problem. The global convergence is established and preliminary numerical results illustrate that the proposed algorithm is efficient and very promising.</p>","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126934266","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}
We consider the equilibrium valuation of currency options with stochastic volatility and systemic co-jumps under the setting of Lucas-type two country economy. Based on the stochastic volatility model in [2], we add an independent jump process and a co-jump process to model the money supply in each country. By solving a partial integro-differential equation (PIDE) for currency options, we can get a closed-form solution for a call currency option price. Compared with the option prices calculated by Monte Carlo method, we show the derived option pricing formula is efficient for practical use. The numerical results show that stochastic volatility and co-jumps have significant impacts on option prices and implied volatilities.
{"title":"Equilibrium valuation of currency options with stochastic volatility and systemic co-jumps","authors":"Yu-hua Xing, Wei Wang, Xiaonan Su, Huawei Niu","doi":"10.3934/jimo.2022022","DOIUrl":"https://doi.org/10.3934/jimo.2022022","url":null,"abstract":"We consider the equilibrium valuation of currency options with stochastic volatility and systemic co-jumps under the setting of Lucas-type two country economy. Based on the stochastic volatility model in [2], we add an independent jump process and a co-jump process to model the money supply in each country. By solving a partial integro-differential equation (PIDE) for currency options, we can get a closed-form solution for a call currency option price. Compared with the option prices calculated by Monte Carlo method, we show the derived option pricing formula is efficient for practical use. The numerical results show that stochastic volatility and co-jumps have significant impacts on option prices and implied volatilities.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124899408","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}
Option pricing under fuzzy environment is a hot research topic nowadays. Traditionally, option pricing were made in the case of fixed interest rate, while the fluctuate of interest rate may result in profit loss or bring unexpected risk. Thus, based on credibility theory, a new option pricing model under fuzzy interest rate are constructed in this paper. In fact, almost all fuzzy option pricing uses expected value method. In this paper, a new pricing method, fuzzy term structure and fuzzy affine term structure method, is adopted, and two European call option pricing formulas are obtained, one is that the fuzzy interest rate coefficients are constants, the other is that the fuzzy interest rate drift coefficient is a fuzzy process.
{"title":"Pricing of European call option under fuzzy interest rate","authors":"C. You, L. Bo","doi":"10.3934/jimo.2022033","DOIUrl":"https://doi.org/10.3934/jimo.2022033","url":null,"abstract":"Option pricing under fuzzy environment is a hot research topic nowadays. Traditionally, option pricing were made in the case of fixed interest rate, while the fluctuate of interest rate may result in profit loss or bring unexpected risk. Thus, based on credibility theory, a new option pricing model under fuzzy interest rate are constructed in this paper. In fact, almost all fuzzy option pricing uses expected value method. In this paper, a new pricing method, fuzzy term structure and fuzzy affine term structure method, is adopted, and two European call option pricing formulas are obtained, one is that the fuzzy interest rate coefficients are constants, the other is that the fuzzy interest rate drift coefficient is a fuzzy process.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121334142","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}
Optimization over Pareto set of a semistrictly quasiconcave vector maximization problem has many applications in economics and technology but it is a challenging task because of the nonconvexity of objective functions and constraint sets. In this article, we propose a novel approach, which is a Branch-and-Bound algorithm for maximizing a composite function begin{document}$ varphi(f(x)) $end{document} over the non-dominated solution set of the begin{document}$ p $end{document}-objective programming problem, where begin{document}$ pgeq 2, p in mathbb{N}, $end{document} the function begin{document}$ varphi $end{document} is increasing and the objective function begin{document}$ f $end{document} is semistrictly quasiconcave. By utilizing the nice properties of Pareto set to define the partitions of branch and bound scheme, the proposed algorithms are promised to be more accurate and efficient than ones using the multi-objective evolutionary approach such as NSGA-III. This is validated by some computational experiments. The Stochastic Portfolio Selection Problem is chosen as an application of our algorithm, where Sharpe ratio is a semistrictly quasiconcave objective function.
Optimization over Pareto set of a semistrictly quasiconcave vector maximization problem has many applications in economics and technology but it is a challenging task because of the nonconvexity of objective functions and constraint sets. In this article, we propose a novel approach, which is a Branch-and-Bound algorithm for maximizing a composite function begin{document}$ varphi(f(x)) $end{document} over the non-dominated solution set of the begin{document}$ p $end{document}-objective programming problem, where begin{document}$ pgeq 2, p in mathbb{N}, $end{document} the function begin{document}$ varphi $end{document} is increasing and the objective function begin{document}$ f $end{document} is semistrictly quasiconcave. By utilizing the nice properties of Pareto set to define the partitions of branch and bound scheme, the proposed algorithms are promised to be more accurate and efficient than ones using the multi-objective evolutionary approach such as NSGA-III. This is validated by some computational experiments. The Stochastic Portfolio Selection Problem is chosen as an application of our algorithm, where Sharpe ratio is a semistrictly quasiconcave objective function.
{"title":"Optimizing over Pareto set of semistrictly quasiconcave vector maximization and application to stochastic portfolio selection","authors":"N. D. Vuong, T. N. Thang","doi":"10.3934/jimo.2022029","DOIUrl":"https://doi.org/10.3934/jimo.2022029","url":null,"abstract":"<p style='text-indent:20px;'>Optimization over Pareto set of a semistrictly quasiconcave vector maximization problem has many applications in economics and technology but it is a challenging task because of the nonconvexity of objective functions and constraint sets. In this article, we propose a novel approach, which is a Branch-and-Bound algorithm for maximizing a composite function <inline-formula><tex-math id=\"M1\">begin{document}$ varphi(f(x)) $end{document}</tex-math></inline-formula> over the non-dominated solution set of the <inline-formula><tex-math id=\"M2\">begin{document}$ p $end{document}</tex-math></inline-formula>-objective programming problem, where <inline-formula><tex-math id=\"M3\">begin{document}$ pgeq 2, p in mathbb{N}, $end{document}</tex-math></inline-formula> the function <inline-formula><tex-math id=\"M4\">begin{document}$ varphi $end{document}</tex-math></inline-formula> is increasing and the objective function <inline-formula><tex-math id=\"M5\">begin{document}$ f $end{document}</tex-math></inline-formula> is semistrictly quasiconcave. By utilizing the nice properties of Pareto set to define the partitions of branch and bound scheme, the proposed algorithms are promised to be more accurate and efficient than ones using the multi-objective evolutionary approach such as NSGA-III. This is validated by some computational experiments. The Stochastic Portfolio Selection Problem is chosen as an application of our algorithm, where Sharpe ratio is a semistrictly quasiconcave objective function.</p>","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123574797","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}
Variable selection and parameter estimation are fundamental and important problems in high dimensional data analysis. In this paper, we employ the hard thresholding regularization method [1] to handle these issues under the framework of high-dimensional and sparse linear regression model. Theoretically, we establish a sharp non-asymptotic estimation error for the global solution and further show that the support of the global solution coincides with the target support with high probability. Motivated by the KKT condition, we propose a primal dual active set algorithm (PDAS) to solve the minimization problem, and show that the proposed PDAS algorithm is essentially a generalized Newton method, which guarantees that the proposed PDAS algorithm will converge fast if a good initial value is provided. Furthermore, we propose a sequential version of the PDAS algorithm (SPDAS) with a warm-start strategy to choose the initial value adaptively. The most significant advantage of the proposed procedure is its fast calculation speed. Extensive numerical studies demonstrate that the proposed method performs well on variable selection and estimation accuracy. It has favorable exhibition over the existing methods in terms of computational speed. As an illustration, we apply the proposed method to a breast cancer gene expression data set.
{"title":"High-dimensional linear regression with hard thresholding regularization: Theory and algorithm","authors":"Lican Kang, Yanming Lai, Yanyan Liu, Yuan Luo, Jing Zhang","doi":"10.3934/jimo.2022034","DOIUrl":"https://doi.org/10.3934/jimo.2022034","url":null,"abstract":"Variable selection and parameter estimation are fundamental and important problems in high dimensional data analysis. In this paper, we employ the hard thresholding regularization method [1] to handle these issues under the framework of high-dimensional and sparse linear regression model. Theoretically, we establish a sharp non-asymptotic estimation error for the global solution and further show that the support of the global solution coincides with the target support with high probability. Motivated by the KKT condition, we propose a primal dual active set algorithm (PDAS) to solve the minimization problem, and show that the proposed PDAS algorithm is essentially a generalized Newton method, which guarantees that the proposed PDAS algorithm will converge fast if a good initial value is provided. Furthermore, we propose a sequential version of the PDAS algorithm (SPDAS) with a warm-start strategy to choose the initial value adaptively. The most significant advantage of the proposed procedure is its fast calculation speed. Extensive numerical studies demonstrate that the proposed method performs well on variable selection and estimation accuracy. It has favorable exhibition over the existing methods in terms of computational speed. As an illustration, we apply the proposed method to a breast cancer gene expression data set.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124910554","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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