Pub Date : 2023-01-01DOI: 10.23952/jnva.7.2023.5.03
{"title":"Further results on quasi efficient solutions in multiobjective optimization","authors":"","doi":"10.23952/jnva.7.2023.5.03","DOIUrl":"https://doi.org/10.23952/jnva.7.2023.5.03","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135909606","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 : 2023-01-01DOI: 10.23952/jnva.7.2023.1.08
{"title":"Optimality conditions of quasi $(alpha,varepsilon)$-solutions and approximate mixed type duality for DC composite optimization problems","authors":"","doi":"10.23952/jnva.7.2023.1.08","DOIUrl":"https://doi.org/10.23952/jnva.7.2023.1.08","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73425909","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 : 2023-01-01DOI: 10.23952/jnva.7.2023.1.09
T. Mewomo, T. O. Alakoya, J. Yao, L. Akinyemi
. The class of quasimonotone variational inequalities is more general and applicable than the class of pseudomonotone and monotone variational inequalities. However, few results can be found in the literature on quasimonotone variational inequalities and currently results are mostly on weak convergent methods in the framework of Hilbert spaces. In this paper, we study the class of non-Lipschitz quasimonotone variational inequalities and the class of non-Lipschitz variational inequalities without monotonicity in the framework of Banach spaces. We propose a new inertial Tseng’s extragradient method and obtain some strong convergence results for the proposed algorithm under some mild conditions on the control parameters. While the cost operator is non-Lipschitz, our proposed method does not require any linesearch procedure but employs a more efficient and simple self-adaptive step sizes with known parameters. Finally, we present several numerical experiments to demonstrate the implementability of our proposed method.
{"title":"Strong convergent inertial Tseng’s extragradient method for solving non-Lipschitz quasimonotone variational inequalities in Banach spaces","authors":"T. Mewomo, T. O. Alakoya, J. Yao, L. Akinyemi","doi":"10.23952/jnva.7.2023.1.09","DOIUrl":"https://doi.org/10.23952/jnva.7.2023.1.09","url":null,"abstract":". The class of quasimonotone variational inequalities is more general and applicable than the class of pseudomonotone and monotone variational inequalities. However, few results can be found in the literature on quasimonotone variational inequalities and currently results are mostly on weak convergent methods in the framework of Hilbert spaces. In this paper, we study the class of non-Lipschitz quasimonotone variational inequalities and the class of non-Lipschitz variational inequalities without monotonicity in the framework of Banach spaces. We propose a new inertial Tseng’s extragradient method and obtain some strong convergence results for the proposed algorithm under some mild conditions on the control parameters. While the cost operator is non-Lipschitz, our proposed method does not require any linesearch procedure but employs a more efficient and simple self-adaptive step sizes with known parameters. Finally, we present several numerical experiments to demonstrate the implementability of our proposed method.","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85711247","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 : 2023-01-01DOI: 10.23952/jnva.7.2023.5.10
{"title":"The generalized conditional gradient method for composite multiobjective optimization problems on Riemannian manifolds","authors":"","doi":"10.23952/jnva.7.2023.5.10","DOIUrl":"https://doi.org/10.23952/jnva.7.2023.5.10","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135909608","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 : 2023-01-01DOI: 10.23952/jnva.7.2023.1.06
{"title":"Convex minimization problems based on an accelerated fixed point algorithm with applications to image restoration problems","authors":"","doi":"10.23952/jnva.7.2023.1.06","DOIUrl":"https://doi.org/10.23952/jnva.7.2023.1.06","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88607567","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 : 2022-10-12DOI: 10.23952/jnva.5.2021.3.10
Xiangling Zhu, Lian Hu, Dan Qu
A family of Dirichlet-Morrey type space D p,λ p−1 is introduced in this paper. For any positive Borel measure μ , the boundedness and compactness of the identity operator Id from D p,λ p−1 to tent spaces T p s (μ) are studied. As an application, the boundedness of the Volttera integral operators Tg and Ig, and the multiplication operator Mg from D p,λ p−1 to the general function space F(p, p− 1−λ ,s) are studied. The essential norm of Tg and Ig are also investigated.
{"title":"Dirichlet-Morrey type spaces and Volterra integral operators","authors":"Xiangling Zhu, Lian Hu, Dan Qu","doi":"10.23952/jnva.5.2021.3.10","DOIUrl":"https://doi.org/10.23952/jnva.5.2021.3.10","url":null,"abstract":"A family of Dirichlet-Morrey type space D p,λ p−1 is introduced in this paper. For any positive Borel measure μ , the boundedness and compactness of the identity operator Id from D p,λ p−1 to tent spaces T p s (μ) are studied. As an application, the boundedness of the Volttera integral operators Tg and Ig, and the multiplication operator Mg from D p,λ p−1 to the general function space F(p, p− 1−λ ,s) are studied. The essential norm of Tg and Ig are also investigated.","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2022-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75834826","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 : 2022-02-15DOI: 10.23952/jnva.7.2023.1.07
M. Jiang, R. Shen, Z. Meng, C. Y. Dang
This paper defines a convertible nonconvex function(CN function for short) and a weak (strong) uniform (decomposable, exact) CN function, proves the optimization conditions for their global solutions and proposes algorithms for solving the unconstrained optimization problems with the decomposable CN function. First, to illustrate the fact that some nonconvex functions, nonsmooth or discontinuous, are actually weak uniform CN functions, examples are given. The operational properties of the CN functions are proved, including addition, subtraction, multiplication, division and compound operations. Second, optimization conditions of the global optimal solution to unconstrained optimization with a weak uniform CN function are proved. Based on the unconstrained optimization problem with the decomposable CN function, a decomposable algorithm is proposed by its augmented Lagrangian penalty function and its convergence is proved. Numerical results show that an approximate global optimal solution to unconstrained optimization with a CN function may be obtained by the decomposable algorithms. The decomposable algorithm can effectively reduce the scale in solving the unconstrained optimization problem with the decomposable CN function. This paper provides a new idea for solving unconstrained nonconvex optimization problems.
{"title":"Optimization conditions and decomposable algorithms for convertible nonconvex optimization","authors":"M. Jiang, R. Shen, Z. Meng, C. Y. Dang","doi":"10.23952/jnva.7.2023.1.07","DOIUrl":"https://doi.org/10.23952/jnva.7.2023.1.07","url":null,"abstract":"This paper defines a convertible nonconvex function(CN function for short) and a weak (strong) uniform (decomposable, exact) CN function, proves the optimization conditions for their global solutions and proposes algorithms for solving the unconstrained optimization problems with the decomposable CN function. First, to illustrate the fact that some nonconvex functions, nonsmooth or discontinuous, are actually weak uniform CN functions, examples are given. The operational properties of the CN functions are proved, including addition, subtraction, multiplication, division and compound operations. Second, optimization conditions of the global optimal solution to unconstrained optimization with a weak uniform CN function are proved. Based on the unconstrained optimization problem with the decomposable CN function, a decomposable algorithm is proposed by its augmented Lagrangian penalty function and its convergence is proved. Numerical results show that an approximate global optimal solution to unconstrained optimization with a CN function may be obtained by the decomposable algorithms. The decomposable algorithm can effectively reduce the scale in solving the unconstrained optimization problem with the decomposable CN function. This paper provides a new idea for solving unconstrained nonconvex optimization problems.","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79396117","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.6.2022.2.01
{"title":"A Special Issue on Recent Trends in Numerical Algorithms and Their Applications","authors":"","doi":"10.23952/jnva.6.2022.2.01","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.2.01","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":"73945919","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.6.2022.4.07
{"title":"Order-preservation properties of resolvent operators and their applications to variational inequalities","authors":"","doi":"10.23952/jnva.6.2022.4.07","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.4.07","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":"77191760","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.6.2022.1.07
A. Latif, Reem Fahad Al Subaie, M. Alansari
. In the setting of metric type spaces, we establish some new results on the existence of fixed points for generalized multi-valued contractive mappings with respect to the w b -distance. In support of our results, some examples are also presented.
{"title":"Fixed points of generalized multi-valued contractive mappings in metric type spaces","authors":"A. Latif, Reem Fahad Al Subaie, M. Alansari","doi":"10.23952/jnva.6.2022.1.07","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.1.07","url":null,"abstract":". In the setting of metric type spaces, we establish some new results on the existence of fixed points for generalized multi-valued contractive mappings with respect to the w b -distance. In support of our results, some examples are also presented.","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":"83707196","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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