Pub Date : 2021-11-06DOI: 10.1142/s0217595922500014
Jun Sun, Lingchen Kong, Mei Li
With the development of modern science and technology, it is easy to obtain a large number of high-dimensional datasets, which are related but different. Classical unimodel analysis is less likely to capture potential links between the different datasets. Recently, a collaborative regression model based on least square (LS) method for this problem has been proposed. In this paper, we propose a robust collaborative regression based on the least absolute deviation (LAD). We give the statistical interpretation of the LS-collaborative regression and LAD-collaborative regression. Then we design an efficient symmetric Gauss–Seidel-based alternating direction method of multipliers algorithm to solve the two models, which has the global convergence and the Q-linear rate of convergence. Finally we report numerical experiments to illustrate the efficiency of the proposed methods.
{"title":"Fast Algorithms for LS and LAD-Collaborative Regression","authors":"Jun Sun, Lingchen Kong, Mei Li","doi":"10.1142/s0217595922500014","DOIUrl":"https://doi.org/10.1142/s0217595922500014","url":null,"abstract":"With the development of modern science and technology, it is easy to obtain a large number of high-dimensional datasets, which are related but different. Classical unimodel analysis is less likely to capture potential links between the different datasets. Recently, a collaborative regression model based on least square (LS) method for this problem has been proposed. In this paper, we propose a robust collaborative regression based on the least absolute deviation (LAD). We give the statistical interpretation of the LS-collaborative regression and LAD-collaborative regression. Then we design an efficient symmetric Gauss–Seidel-based alternating direction method of multipliers algorithm to solve the two models, which has the global convergence and the Q-linear rate of convergence. Finally we report numerical experiments to illustrate the efficiency of the proposed methods.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"58 1","pages":"2250001:1-2250001:29"},"PeriodicalIF":0.0,"publicationDate":"2021-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86578002","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 : 2021-11-03DOI: 10.1142/s0217595921500470
Guolin Yu, Siqi Li, Xiaosu Pan, Wenyan Han
This paper is devoted to the investigation of optimality conditions for approximate quasi-weakly efficient solutions to a class of nonsmooth Vector Equilibrium Problem (VEP) via convexificators. First, a necessary optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is presented by making use of the properties of convexificators. Second, the notion of approximate pseudoconvex function in the form of convexificators is introduced, and its existence is verified by a concrete example. Under the introduced generalized convexity assumption, a sufficient optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is also established. Finally, a scalar characterization for approximate quasi-weakly efficient solutions to problem (VEP) is obtained by taking advantage of Tammer’s function.
{"title":"Optimality of Approximate Quasi-Weakly Efficient Solutions for Vector Equilibrium Problems via Convexificators","authors":"Guolin Yu, Siqi Li, Xiaosu Pan, Wenyan Han","doi":"10.1142/s0217595921500470","DOIUrl":"https://doi.org/10.1142/s0217595921500470","url":null,"abstract":"This paper is devoted to the investigation of optimality conditions for approximate quasi-weakly efficient solutions to a class of nonsmooth Vector Equilibrium Problem (VEP) via convexificators. First, a necessary optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is presented by making use of the properties of convexificators. Second, the notion of approximate pseudoconvex function in the form of convexificators is introduced, and its existence is verified by a concrete example. Under the introduced generalized convexity assumption, a sufficient optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is also established. Finally, a scalar characterization for approximate quasi-weakly efficient solutions to problem (VEP) is obtained by taking advantage of Tammer’s function.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"30 1","pages":"2150047:1-2150047:16"},"PeriodicalIF":0.0,"publicationDate":"2021-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74833044","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 : 2021-10-27DOI: 10.1142/s0217595922500038
Wenxin Du, Shenglong Hu, Youyicun Lin, Jie Wang
{"title":"A Global Convergence Analysis for Computing a Symmetric Low-Rank Orthogonal Approximation","authors":"Wenxin Du, Shenglong Hu, Youyicun Lin, Jie Wang","doi":"10.1142/s0217595922500038","DOIUrl":"https://doi.org/10.1142/s0217595922500038","url":null,"abstract":"","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"7 1","pages":"2250003:1-2250003:12"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76980080","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 : 2021-10-02DOI: 10.1142/s0217595921500421
Merve Sözen, M. Cengiz
Data envelopment analysis (DEA) is a method that finds the effectiveness of an existing system using a number of input and output variables. In this study, we obtained energy efficiencies of construction, industrial, power, and transportation sectors in OECD countries for 2011 using DEA. It is possible to achieve the efficiencies in different sectors. However, we aim to find joint energy efficiency scores for all sectors. One of the methods proposed in the literature to obtain joint efficiency is network data envelopment analysis (network DEA). Network DEA treats sectors as sub-processes and obtains system and process efficiencies through optimal weights. Alternatively, we used a novel copula-based approach to achieve common efficiency scores. In this approach, it is possible to demonstrate the dependency structure between the efficiency scores of similar qualities obtained with DEA by copula families. New efficiency scores are obtained with the help of joint probability distribution. Then, we obtained joint efficiency scores through the copula approach using these efficiency scores. Finally, we obtained the joint efficiency scores of the same sectors through network DEA. As a result, we compared network DEA with the copula approach and interpreted the efficiencies of each energy sector and joint efficiencies.
{"title":"Copula Approach to Multivariate Energy Efficiency Analysis","authors":"Merve Sözen, M. Cengiz","doi":"10.1142/s0217595921500421","DOIUrl":"https://doi.org/10.1142/s0217595921500421","url":null,"abstract":"Data envelopment analysis (DEA) is a method that finds the effectiveness of an existing system using a number of input and output variables. In this study, we obtained energy efficiencies of construction, industrial, power, and transportation sectors in OECD countries for 2011 using DEA. It is possible to achieve the efficiencies in different sectors. However, we aim to find joint energy efficiency scores for all sectors. One of the methods proposed in the literature to obtain joint efficiency is network data envelopment analysis (network DEA). Network DEA treats sectors as sub-processes and obtains system and process efficiencies through optimal weights. Alternatively, we used a novel copula-based approach to achieve common efficiency scores. In this approach, it is possible to demonstrate the dependency structure between the efficiency scores of similar qualities obtained with DEA by copula families. New efficiency scores are obtained with the help of joint probability distribution. Then, we obtained joint efficiency scores through the copula approach using these efficiency scores. Finally, we obtained the joint efficiency scores of the same sectors through network DEA. As a result, we compared network DEA with the copula approach and interpreted the efficiencies of each energy sector and joint efficiencies.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"6 1","pages":"2150042:1-2150042:13"},"PeriodicalIF":0.0,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90635940","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 : 2021-09-28DOI: 10.1142/s0217595921500433
Liping Zhang, S. Du
A new exchange method is presented for semi-infinite optimization problems with polyhedron constraints. The basic idea is to use an active set strategy as exchange rule to construct an approximate problem with finitely many constraints at each iteration. Under mild conditions, we prove that the proposed algorithm terminates in a finite number of iterations and guarantees that the solution of the resulting approximate problem at final iteration converges to the solution of the original problem within arbitrarily given tolerance. Numerical results indicate that the proposed algorithm is efficient and promising.
{"title":"On Exchange Methods for Nonlinear Semi-Infinite Programs","authors":"Liping Zhang, S. Du","doi":"10.1142/s0217595921500433","DOIUrl":"https://doi.org/10.1142/s0217595921500433","url":null,"abstract":"A new exchange method is presented for semi-infinite optimization problems with polyhedron constraints. The basic idea is to use an active set strategy as exchange rule to construct an approximate problem with finitely many constraints at each iteration. Under mild conditions, we prove that the proposed algorithm terminates in a finite number of iterations and guarantees that the solution of the resulting approximate problem at final iteration converges to the solution of the original problem within arbitrarily given tolerance. Numerical results indicate that the proposed algorithm is efficient and promising.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"87 1","pages":"2150043:1-2150043:26"},"PeriodicalIF":0.0,"publicationDate":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72802248","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 : 2021-09-21DOI: 10.1142/s0217595921500469
Xiao-Lin Zhao, Jian Xu, Ji-Bo Wang, Lin Li
{"title":"Bicriteria Common Flow Allowance Scheduling with Aging Effect, Convex Resource Allocation, and a Rate-Modifying Activity on a Single Machine","authors":"Xiao-Lin Zhao, Jian Xu, Ji-Bo Wang, Lin Li","doi":"10.1142/s0217595921500469","DOIUrl":"https://doi.org/10.1142/s0217595921500469","url":null,"abstract":"","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"12 1","pages":"2150046:1-2150046:21"},"PeriodicalIF":0.0,"publicationDate":"2021-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91535709","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 : 2021-09-08DOI: 10.1142/s021759592150041x
Yu Tian
In this study, the due-window assignment single-machine scheduling problem with resource allocation is considered, where the processing time of a job is controllable as a linear or convex function of amount of resource allocated to the job. Under common due-window and slack due-window assignments, our goal is to determine the optimal sequence of all jobs, the due-window start time, due-window size, and optimal resource allocation such that a sum of the scheduling cost (including weighted earliness/tardiness penalty, weighted number of early and tardy job, weighted due-window start time, and due-window size) and resource consumption cost is minimized. We analyze the optimality properties, and provide polynomial time solutions to solve the problem under four versions of due-window assignment and resource allocation function.
{"title":"Single-Machine Due-Window Assignment Scheduling with Resource Allocation and Generalized Earliness/Tardiness Penalties","authors":"Yu Tian","doi":"10.1142/s021759592150041x","DOIUrl":"https://doi.org/10.1142/s021759592150041x","url":null,"abstract":"In this study, the due-window assignment single-machine scheduling problem with resource allocation is considered, where the processing time of a job is controllable as a linear or convex function of amount of resource allocated to the job. Under common due-window and slack due-window assignments, our goal is to determine the optimal sequence of all jobs, the due-window start time, due-window size, and optimal resource allocation such that a sum of the scheduling cost (including weighted earliness/tardiness penalty, weighted number of early and tardy job, weighted due-window start time, and due-window size) and resource consumption cost is minimized. We analyze the optimality properties, and provide polynomial time solutions to solve the problem under four versions of due-window assignment and resource allocation function.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"53 1","pages":"2150041:1-2150041:16"},"PeriodicalIF":0.0,"publicationDate":"2021-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81121580","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 : 2021-08-31DOI: 10.1142/s021759592150038x
Yunxin Luo, Chenchen Wu, Chunming Xu
In this paper, the problem we study is how to maximize a monotone non-submodular function with cardinality constraint. Different from the previous streaming algorithms, this paper mainly considers the sliding window model. Based on the concept of diminishing-return ratio [Formula: see text], we propose a [Formula: see text]-approximation algorithm with the memory [Formula: see text], where [Formula: see text] is the ratio between maximum and minimum values of any singleton element of function [Formula: see text]. Then, we improve the approximation ratio to [Formula: see text] through the sub-windows at the expense of losing some memory. Our results generalize the corresponding results for the submodular case.
{"title":"Approximation Algorithms for Non-Submodular Optimization Over Sliding Windows","authors":"Yunxin Luo, Chenchen Wu, Chunming Xu","doi":"10.1142/s021759592150038x","DOIUrl":"https://doi.org/10.1142/s021759592150038x","url":null,"abstract":"In this paper, the problem we study is how to maximize a monotone non-submodular function with cardinality constraint. Different from the previous streaming algorithms, this paper mainly considers the sliding window model. Based on the concept of diminishing-return ratio [Formula: see text], we propose a [Formula: see text]-approximation algorithm with the memory [Formula: see text], where [Formula: see text] is the ratio between maximum and minimum values of any singleton element of function [Formula: see text]. Then, we improve the approximation ratio to [Formula: see text] through the sub-windows at the expense of losing some memory. Our results generalize the corresponding results for the submodular case.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"221 1","pages":"2150038:1-2150038:20"},"PeriodicalIF":0.0,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89135108","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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