Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.2.04
{"title":"Multi-objective optimization of a nonlinear batch time-delay system with minimum system sensitivity","authors":"","doi":"10.23952/jnva.6.2022.2.04","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.2.04","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89725934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.2.09
{"title":"Coderivatives and Aubin properties of solution mappings for parametric vector variational inequality problems","authors":"","doi":"10.23952/jnva.6.2022.2.09","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.2.09","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75329105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.2.02
K. Guo, C. Zhu, K. Guo, C. Zhu
. In this paper, we study a Bregman proximal point algorithm (BPPA) for convex optimization problems. Though the convergence and sublinear convergence rate for BPPA are well-understand, the linear convergence rate for BPPA has yet been thoroughly studied in the literature. In this paper, we analyze the linear convergence rate of BPPA. Under the assumption that the objective function is strongly convex relative to a Legendre function, we establish the linear convergence for the function values sequence. Moreover, if the Legendre function is strongly convex and smooth, the linear convergence for the iterative sequence of BPPA is obtained.
{"title":"On the linear convergence of a Bregman proximal point algorithm","authors":"K. Guo, C. Zhu, K. Guo, C. Zhu","doi":"10.23952/jnva.6.2022.2.02","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.2.02","url":null,"abstract":". In this paper, we study a Bregman proximal point algorithm (BPPA) for convex optimization problems. Though the convergence and sublinear convergence rate for BPPA are well-understand, the linear convergence rate for BPPA has yet been thoroughly studied in the literature. In this paper, we analyze the linear convergence rate of BPPA. Under the assumption that the objective function is strongly convex relative to a Legendre function, we establish the linear convergence for the function values sequence. Moreover, if the Legendre function is strongly convex and smooth, the linear convergence for the iterative sequence of BPPA is obtained.","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83325874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.5.04
{"title":"A deep neural network-based numerical method for solving contact problems","authors":"","doi":"10.23952/jnva.6.2022.5.04","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.5.04","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90234512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.5.09
H. Rong, M. Sofonea
. We consider an elliptic variational-hemivariational inequality P in a p -uniformly smooth Banach space. We prove that the inequality is governed by a multivalued maximal monotone operator, and, for each λ > 0, we use the resolvent of this operator to construct an auxiliary fixed point problem, denoted P λ . Next, we perform a parallel study of problems P and P λ based on their intrinsic equivalence. In this way, we prove existence, uniqueness, and well-posedness results with respect to specific Tykhonov triples. The existence of a unique common solution to problems P and P λ is proved by using the Banach contraction principle in the study of Problem P λ . In contrast, the well-posedness of the problems is obtained by using a monotonicity argument in the study of Problem P . Finally, the properties of Problem P λ allow us to deduce a convergence criterion in the study of Problem P .
{"title":"On the well-posedness of variational-hemivariational inequalities and associated fixed point problems","authors":"H. Rong, M. Sofonea","doi":"10.23952/jnva.6.2022.5.09","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.5.09","url":null,"abstract":". We consider an elliptic variational-hemivariational inequality P in a p -uniformly smooth Banach space. We prove that the inequality is governed by a multivalued maximal monotone operator, and, for each λ > 0, we use the resolvent of this operator to construct an auxiliary fixed point problem, denoted P λ . Next, we perform a parallel study of problems P and P λ based on their intrinsic equivalence. In this way, we prove existence, uniqueness, and well-posedness results with respect to specific Tykhonov triples. The existence of a unique common solution to problems P and P λ is proved by using the Banach contraction principle in the study of Problem P λ . In contrast, the well-posedness of the problems is obtained by using a monotonicity argument in the study of Problem P . Finally, the properties of Problem P λ allow us to deduce a convergence criterion in the study of Problem P .","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89216519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.3.05
{"title":"Visual transfer for reinforcement learning via gradient penalty based Wasserstein domain confusion","authors":"","doi":"10.23952/jnva.6.2022.3.05","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.3.05","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77710623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.1.02
Xiang Zhu, Zhiling Cai, Y. Ziniu, Junliang Wu, William Zhu
. As one of the mainstream clustering methods, the spectral clustering has aroused more and more attention recently because of its good performance, especially in nonlinear data sets. However, traditional spectral clustering models have high computational complexity. Meanwhile, most of these models fail in distinguishing the noisy and useful features in practice, which leads to the limitation of clustering performance. In this paper, we propose a new fast spectral clustering with self-weighted features (FSCSWF) to achieve good clustering performance through learning and assigning optimal weights for features in a low computational complexity. Specifically, the FSCSWF selects anchors from original samples, then learns the weights of features and the similarity between anchors and samples interactively in a local structure learning framework. This interactive learning makes the learnt similarity can better measure the relationship between anchors, and samples due to the optimal weights make the data points become more discriminative. Moreover, the connectivity constraint are embedded to make sure that the connected components of bipartite graph constructed by the learnt similarity can indicate clusters di-rectly. In this way, the FSCSWF can achieve good clustering performance and has a low computational complexity, which is linear to the number of samples. Extensive experiments on synthetic and practical data sets illustrate the effectiveness and efficiency of the FSCSWF with respect to state-of-the-art methods.
{"title":"Fast spectral clustering with self-weighted features","authors":"Xiang Zhu, Zhiling Cai, Y. Ziniu, Junliang Wu, William Zhu","doi":"10.23952/jnva.6.2022.1.02","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.1.02","url":null,"abstract":". As one of the mainstream clustering methods, the spectral clustering has aroused more and more attention recently because of its good performance, especially in nonlinear data sets. However, traditional spectral clustering models have high computational complexity. Meanwhile, most of these models fail in distinguishing the noisy and useful features in practice, which leads to the limitation of clustering performance. In this paper, we propose a new fast spectral clustering with self-weighted features (FSCSWF) to achieve good clustering performance through learning and assigning optimal weights for features in a low computational complexity. Specifically, the FSCSWF selects anchors from original samples, then learns the weights of features and the similarity between anchors and samples interactively in a local structure learning framework. This interactive learning makes the learnt similarity can better measure the relationship between anchors, and samples due to the optimal weights make the data points become more discriminative. Moreover, the connectivity constraint are embedded to make sure that the connected components of bipartite graph constructed by the learnt similarity can indicate clusters di-rectly. In this way, the FSCSWF can achieve good clustering performance and has a low computational complexity, which is linear to the number of samples. Extensive experiments on synthetic and practical data sets illustrate the effectiveness and efficiency of the FSCSWF with respect to state-of-the-art methods.","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82616710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.5.01
{"title":"A Special Issue on Variational and Hemivariational Inequalities with Applications","authors":"","doi":"10.23952/jnva.6.2022.5.01","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.5.01","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90210654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.4.05
{"title":"Viscosity and inertial algorithms for the split common fixed point problem with applications to compressed sensing","authors":"","doi":"10.23952/jnva.6.2022.4.05","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.4.05","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90957190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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