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.6.2022.4.02
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}
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.6.2022.5.10
{"title":"Some qualitative properties of solutions of higher-order lower semicontinus differential inclusions","authors":"","doi":"10.23952/jnva.6.2022.5.10","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.5.10","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"2 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73382692","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.6.2022.3.02
{"title":"On semilinear fractional differential inclusions with a nonconvex-valued right-hand side in Banach spaces","authors":"","doi":"10.23952/jnva.6.2022.3.02","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.3.02","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"36 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85806380","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.6.2022.2.05
{"title":"Linear fractional optimization problems on Jordan Euclidean algebras","authors":"","doi":"10.23952/jnva.6.2022.2.05","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.2.05","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76053576","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.6.2022.1.05
{"title":"A certain class of $theta_{L}$-type non-linear operators and some related fixed point results","authors":"","doi":"10.23952/jnva.6.2022.1.05","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.1.05","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"36 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78053001","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.6.2022.5.07
{"title":"Simultaneous distributed and Neumann boundary optimal control problems for elliptic hemivariational inequalities","authors":"","doi":"10.23952/jnva.6.2022.5.07","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.5.07","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"118 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77427945","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.6.2022.5.02
{"title":"Viscoelastic elliptic membrane shells on bilateral frictional contact: An asymptotic approach","authors":"","doi":"10.23952/jnva.6.2022.5.02","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.5.02","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"57 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88010273","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 : 2021-08-17DOI: 10.23952/jnva.5.2021.6.01
N. K. Son, N. N. Thieu, N. D. Yen
In the setting adopted by Edmond and Thibault [Relaxation of an optimal control problem involving a perturbed sweeping process, Math. Program. 104 (2005), 347-373], we study a class of perturbed sweeping processes. Under suitable assumptions, we obtain two solution existence theorems for the perturbed sweeping processes with the constraint sets being prox-regular sublevel sets. The results are applied to the behavior of some concrete mechanical sweeping processes, which appear for the first time in this paper.
{"title":"On the solution existence for prox-regular perturbed sweeping processes","authors":"N. K. Son, N. N. Thieu, N. D. Yen","doi":"10.23952/jnva.5.2021.6.01","DOIUrl":"https://doi.org/10.23952/jnva.5.2021.6.01","url":null,"abstract":"In the setting adopted by Edmond and Thibault [Relaxation of an optimal control problem involving a perturbed sweeping process, Math. Program. 104 (2005), 347-373], we study a class of perturbed sweeping processes. Under suitable assumptions, we obtain two solution existence theorems for the perturbed sweeping processes with the constraint sets being prox-regular sublevel sets. The results are applied to the behavior of some concrete mechanical sweeping processes, which appear for the first time in this paper.","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"170 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76643142","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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