Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.2.07
{"title":"Approximate elements for set optimization problems with respect to variable domination structures","authors":"","doi":"10.23952/jnva.6.2022.2.07","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.2.07","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"51 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90658832","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.6.2022.3.03
{"title":"Local convergence of the Newton’s method in two step nilpotent Lie groups","authors":"","doi":"10.23952/jnva.6.2022.3.03","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.3.03","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"43 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86076293","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.6.2022.6.02
{"title":"A steepest descent-like method for vector optimization problems with variable domination structure","authors":"","doi":"10.23952/jnva.6.2022.6.02","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.6.02","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"134 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79409288","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.6.2022.2.06
{"title":"Constraint qualifications in nonsmooth optimization: Classification and inter-relations","authors":"","doi":"10.23952/jnva.6.2022.2.06","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.2.06","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"27 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80324011","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.6.2022.1.03
Xu Hong-kun, N. Altwaijry, I. Alzughaibi, S. Chebbi
We extend the viscosity approximation method (VAM) to accretive operators (via their resolvents) in a uniformly convex and/or uniformly Gâteaux differentiable Banach space X to find a zero of an m-accretive operator and of the sum of two m-accretive operators. In all cases, we prove the strong convergence of our VAM algorithms and the limit of the iterates is identified as the unique sunny nonexpansive retraction onto to the zero set of the operator.
{"title":"The viscosity approximation method for accretive operators in Banach spaces","authors":"Xu Hong-kun, N. Altwaijry, I. Alzughaibi, S. Chebbi","doi":"10.23952/jnva.6.2022.1.03","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.1.03","url":null,"abstract":"We extend the viscosity approximation method (VAM) to accretive operators (via their resolvents) in a uniformly convex and/or uniformly Gâteaux differentiable Banach space X to find a zero of an m-accretive operator and of the sum of two m-accretive operators. In all cases, we prove the strong convergence of our VAM algorithms and the limit of the iterates is identified as the unique sunny nonexpansive retraction onto to the zero set of the operator.","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"518 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77168688","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.6.2022.5.05
{"title":"Existence of solutions to a new class of coupled variational-hemivariational inequalities","authors":"","doi":"10.23952/jnva.6.2022.5.05","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.5.05","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"12 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84848709","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.6.2022.6.06
{"title":"A trust-region interior-point technique to solve multi-objective optimization problems and its application to a tuberculosis optimal control problem","authors":"","doi":"10.23952/jnva.6.2022.6.06","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.6.06","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"11 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89801124","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.6.2022.1.04
H. Rehman, P. Kumam, Y. Shehu, Murat Ozdemir, W. Kumam
In this paper, we introduce a modification of the extragradient algorithm with a non-monotonic stepsize rule to solve equilibrium problems. This modification is based on the inertial subgradient technique. Under mild conditions, such as, the Lipschitz continuity and the monotonicity of a bifunction (including the pseudomonotonicity), the strong convergence of the proposed algorithm is established in a real Hilbert space. The proposed algorithm uses a non-monotonic stepsize rule based on the local bifunction information rather than its Lipschitz-type constants or other line search methods. We present various numerical examples, which illustrate the strong convergence of the algorithm.
{"title":"An inertial non-monotonic self-adaptive iterative algorithm for solving equilibrium problems","authors":"H. Rehman, P. Kumam, Y. Shehu, Murat Ozdemir, W. Kumam","doi":"10.23952/jnva.6.2022.1.04","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.1.04","url":null,"abstract":"In this paper, we introduce a modification of the extragradient algorithm with a non-monotonic stepsize rule to solve equilibrium problems. This modification is based on the inertial subgradient technique. Under mild conditions, such as, the Lipschitz continuity and the monotonicity of a bifunction (including the pseudomonotonicity), the strong convergence of the proposed algorithm is established in a real Hilbert space. The proposed algorithm uses a non-monotonic stepsize rule based on the local bifunction information rather than its Lipschitz-type constants or other line search methods. We present various numerical examples, which illustrate the strong convergence of the algorithm.","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"160 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74499491","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.6.2022.6.08
{"title":"A new accelerated positive-indefinite proximal ADMM for constrained separable convex optimization problems","authors":"","doi":"10.23952/jnva.6.2022.6.08","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.6.08","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"48 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76422325","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.6.2022.4.02
Yaxuan Zhang, Li Yingying
. In this paper, we present a relaxed CQ algorithm involving the Armijo-line search and the alternated inertial technique to solve the multiple-sets split feasibility problem in infinite dimensional real Hilbert spaces. We prove the convergence of the sequence generated by our method under some mild assumptions. Finally, numerical simulations show the efficiency of our algorithm.
{"title":"A relaxed CQ algorithm involving the alternated inertial technique for the multiple-sets split feasibility problem","authors":"Yaxuan Zhang, Li Yingying","doi":"10.23952/jnva.6.2022.4.02","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.4.02","url":null,"abstract":". In this paper, we present a relaxed CQ algorithm involving the Armijo-line search and the alternated inertial technique to solve the multiple-sets split feasibility problem in infinite dimensional real Hilbert spaces. We prove the convergence of the sequence generated by our method under some mild assumptions. Finally, numerical simulations show the efficiency of our algorithm.","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"137 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78041791","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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