In this paper, we present a novel regularization with a truncated difference of nuclear norm and Frobenius norm of form begin{document}$ L_{t,*-alpha F} $end{document} with an integer begin{document}$ t $end{document} and parameter begin{document}$ alpha $end{document} for rank minimization problem. The forward-backward splitting (FBS) algorithm is proposed to solve such a regularization problem, whose subproblems are shown to have closed-form solutions. We show that any accumulation point of the sequence generated by the FBS algorithm is a first-order stationary point. In the end, the numerical results demonstrate that the proposed FBS algorithm outperforms the existing methods.
In this paper, we present a novel regularization with a truncated difference of nuclear norm and Frobenius norm of form begin{document}$ L_{t,*-alpha F} $end{document} with an integer begin{document}$ t $end{document} and parameter begin{document}$ alpha $end{document} for rank minimization problem. The forward-backward splitting (FBS) algorithm is proposed to solve such a regularization problem, whose subproblems are shown to have closed-form solutions. We show that any accumulation point of the sequence generated by the FBS algorithm is a first-order stationary point. In the end, the numerical results demonstrate that the proposed FBS algorithm outperforms the existing methods.
{"title":"Low rank matrix minimization with a truncated difference of nuclear norm and Frobenius norm regularization","authors":"Huiyuan Guo, Quan Yu, Xinzhen Zhang, Lulu Cheng","doi":"10.3934/jimo.2022045","DOIUrl":"https://doi.org/10.3934/jimo.2022045","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we present a novel regularization with a truncated difference of nuclear norm and Frobenius norm of form <inline-formula><tex-math id=\"M1\">begin{document}$ L_{t,*-alpha F} $end{document}</tex-math></inline-formula> with an integer <inline-formula><tex-math id=\"M2\">begin{document}$ t $end{document}</tex-math></inline-formula> and parameter <inline-formula><tex-math id=\"M3\">begin{document}$ alpha $end{document}</tex-math></inline-formula> for rank minimization problem. The forward-backward splitting (FBS) algorithm is proposed to solve such a regularization problem, whose subproblems are shown to have closed-form solutions. We show that any accumulation point of the sequence generated by the FBS algorithm is a first-order stationary point. In the end, the numerical results demonstrate that the proposed FBS algorithm outperforms the existing methods.</p>","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"54 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":"127238183","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}
Recently, Synthetic Minority Over-Sampling Technique (SMOTE) has been widely used to handle the imbalanced classification. To address the issues of existing benchmark methods, we propose a novel scheme of SMOTE based on the K-means and Intuitionistic Fuzzy Set theory to assign proper weights to the existing points and generate new synthetic points from them. Besides, we introduce the state-of-the-art kernel-free fuzzy quadratic surface support vector machine (QSSVM) to do the classification. Finally, the numerical experiments on various artificial and real data sets strongly demonstrate the validity and applicability of our proposed method, especially in the presence of mislabeled information.
{"title":"A SMOTE-based quadratic surface support vector machine for imbalanced classification with mislabeled information","authors":"Qianru Zhai, Ye Tian, Jingyue Zhou","doi":"10.3934/jimo.2021230","DOIUrl":"https://doi.org/10.3934/jimo.2021230","url":null,"abstract":"Recently, Synthetic Minority Over-Sampling Technique (SMOTE) has been widely used to handle the imbalanced classification. To address the issues of existing benchmark methods, we propose a novel scheme of SMOTE based on the K-means and Intuitionistic Fuzzy Set theory to assign proper weights to the existing points and generate new synthetic points from them. Besides, we introduce the state-of-the-art kernel-free fuzzy quadratic surface support vector machine (QSSVM) to do the classification. Finally, the numerical experiments on various artificial and real data sets strongly demonstrate the validity and applicability of our proposed method, especially in the presence of mislabeled information.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"1 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":"128936738","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}
Aiming at the energy management problem of unmanned aerial vehicles (UAVs) in the terminal area energy management (TAEM) phase, a real-time online trajectory planning and guidance strategy based on judging energy is proposed. The trajectory planning strategy estimates the flight profile online in real time by judging the energy and changing the radius of the heading alignment circle. In addition, guidance instructions are also obtained at once. In the S-turn stage, the lateral guidance adopts a closed loop control mode with a fixed bank angle. In the remaining stage, the lateral guidance adopts a closed loop control mode for tracking the azimuth angle. In all stages, the longitudinal guidance adopts a closed loop control mode for tracking the flight path angle and flight height. The trajectory planning strategy is able to quickly generate a reference trajectory for testing cases with large variations not only in the initial energy but also in the energy of the flight process. The simulation results show that the proposed trajectory planning and guidance strategy can effectively manage a UAV's energy in the TAEM phase, ensuring that the UAV lands safely.
{"title":"Real-time online trajectory planning and guidance for terminal area energy management of unmanned aerial vehicle","authors":"Xiaoyong Mao, Baoguo Yu, Yingjing Shi, Rui Li","doi":"10.3934/jimo.2022026","DOIUrl":"https://doi.org/10.3934/jimo.2022026","url":null,"abstract":"Aiming at the energy management problem of unmanned aerial vehicles (UAVs) in the terminal area energy management (TAEM) phase, a real-time online trajectory planning and guidance strategy based on judging energy is proposed. The trajectory planning strategy estimates the flight profile online in real time by judging the energy and changing the radius of the heading alignment circle. In addition, guidance instructions are also obtained at once. In the S-turn stage, the lateral guidance adopts a closed loop control mode with a fixed bank angle. In the remaining stage, the lateral guidance adopts a closed loop control mode for tracking the azimuth angle. In all stages, the longitudinal guidance adopts a closed loop control mode for tracking the flight path angle and flight height. The trajectory planning strategy is able to quickly generate a reference trajectory for testing cases with large variations not only in the initial energy but also in the energy of the flight process. The simulation results show that the proposed trajectory planning and guidance strategy can effectively manage a UAV's energy in the TAEM phase, ensuring that the UAV lands safely.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"1 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":"121455681","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 explores a production inventory model considering two high-tech products of the same kind. One is the primary product and the other is the updated version of that primary product. Due to continuous development in technology, the life-cycle of some high-tech products, like, smartphone, tablet, laptop, etc. have become shorter. We witness the launching of new products more frequently in this field. This prompts the manufacturers to release an updated or pro version of their existing products after a certain time to compete in the market. The reputation of the primary product (in terms of quality and performance) plays an important role in generating the demand for the updated product. Due to the short life-cycle of the products, the proposed model considers only two consecutive production runs. One for the primary product and one for the updated product. Here the demands of both the products depend on the respective selling prices. Moreover, the demand of the updated product is also dependent on the quality of the primary product. Shortages for the primary product are allowed. Those shortages are backlogged partially with the updated product. Also, the possibility of imperfect production during regular production runs is considered. The selling prices, production rates, and the production run times for both the products are considered here as decision variables. Due to the complexity in the resulting optimization problem, the quantum-behaved particle swarm optimization technique is applied to derive the optimal profit. The concavity natures of the profit function are shown graphically. A numerical illustration is presented for the economic validation of the model. Finally, sensitivity analysis of the optimal solutions concerning the key inventory parameters is conducted for identifying several managerial implications.
{"title":"A production inventory model for high-tech products involving two production runs and a product variation","authors":"Subhendu Ruidas, M. R. Seikh, P. Nayak","doi":"10.3934/jimo.2022038","DOIUrl":"https://doi.org/10.3934/jimo.2022038","url":null,"abstract":"This paper explores a production inventory model considering two high-tech products of the same kind. One is the primary product and the other is the updated version of that primary product. Due to continuous development in technology, the life-cycle of some high-tech products, like, smartphone, tablet, laptop, etc. have become shorter. We witness the launching of new products more frequently in this field. This prompts the manufacturers to release an updated or pro version of their existing products after a certain time to compete in the market. The reputation of the primary product (in terms of quality and performance) plays an important role in generating the demand for the updated product. Due to the short life-cycle of the products, the proposed model considers only two consecutive production runs. One for the primary product and one for the updated product. Here the demands of both the products depend on the respective selling prices. Moreover, the demand of the updated product is also dependent on the quality of the primary product. Shortages for the primary product are allowed. Those shortages are backlogged partially with the updated product. Also, the possibility of imperfect production during regular production runs is considered. The selling prices, production rates, and the production run times for both the products are considered here as decision variables. Due to the complexity in the resulting optimization problem, the quantum-behaved particle swarm optimization technique is applied to derive the optimal profit. The concavity natures of the profit function are shown graphically. A numerical illustration is presented for the economic validation of the model. Finally, sensitivity analysis of the optimal solutions concerning the key inventory parameters is conducted for identifying several managerial implications.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"22 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":"132751770","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, fractional continuous-time programming problems with inequality phase constraints are considered. Optimality conditions and duality results under a certain regularity condition are derived. All functions are assumed to be nondifferentiable. These results improve and generalize a number of existing results in the area of fractional continuous-time programming. We provide a practical example to illustrate our results.
{"title":"Saddle-point type optimality criteria, duality and a new approach for solving nonsmooth fractional continuous-time programming problems","authors":"Aleksandar Jović","doi":"10.3934/jimo.2022025","DOIUrl":"https://doi.org/10.3934/jimo.2022025","url":null,"abstract":"In this paper, fractional continuous-time programming problems with inequality phase constraints are considered. Optimality conditions and duality results under a certain regularity condition are derived. All functions are assumed to be nondifferentiable. These results improve and generalize a number of existing results in the area of fractional continuous-time programming. We provide a practical example to illustrate our results.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"61 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":"133116014","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 investigates the issue of information leakage in a supply consisting of one manufacturer, one incumbent retailer endowed with superior demand information, and a capital-constrained entrant retailer financed by the manufacturer's trade credit. The incumbent retailer faces the situation that the manufacturer may leak the incumbent retailer's order information to the uninformed entrant retailer. We first examine whether trade credit can prevent information leakage. It shows that the manufacturer always leaks information in the non-bankruptcy scenario where the capital-constrained retailer does not go bankrupt in the low-demand state. In contrast, in the bankruptcy scenario, the manufacturer does not leak information since it could get more transfer revenue from the bankrupt entrant retailer than the revenue obtained from the incumbent retailer. We also explore the impacts of information leakage on each member's optimal decision and profit. Interestingly, the findings show that the informed incumbent retailer, taking the advantage of being the first-mover, is able to actively place a larger order to induce the manufacturer to leak information and benefits from information leakage under certain conditions.
{"title":"Trade credit and information leakage in a supply chain with competing retailers","authors":"Man Yu, Erbao Cao","doi":"10.3934/jimo.2022042","DOIUrl":"https://doi.org/10.3934/jimo.2022042","url":null,"abstract":"This paper investigates the issue of information leakage in a supply consisting of one manufacturer, one incumbent retailer endowed with superior demand information, and a capital-constrained entrant retailer financed by the manufacturer's trade credit. The incumbent retailer faces the situation that the manufacturer may leak the incumbent retailer's order information to the uninformed entrant retailer. We first examine whether trade credit can prevent information leakage. It shows that the manufacturer always leaks information in the non-bankruptcy scenario where the capital-constrained retailer does not go bankrupt in the low-demand state. In contrast, in the bankruptcy scenario, the manufacturer does not leak information since it could get more transfer revenue from the bankrupt entrant retailer than the revenue obtained from the incumbent retailer. We also explore the impacts of information leakage on each member's optimal decision and profit. Interestingly, the findings show that the informed incumbent retailer, taking the advantage of being the first-mover, is able to actively place a larger order to induce the manufacturer to leak information and benefits from information leakage under certain conditions.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"38 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":"116026772","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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