In this paper, we extend the class of strongly $E$-preinvex and strongly $E$-invex functions to quasi strongly $E$-preinvex, quasi strongly $E$-invex and pseudo strongly $E$-invex functions. Some nontrivial suitable examples have been constructed in support of our definitions. Several interesting properties and relationships of these functions are discussed. Furthermore, to show the application of our results, we consider a nonlinear programming problem and show that the local minimum point is also a strictly global minimum.
{"title":"Quasi Strongly $ E $-preinvexity and its relationships with non-linear programming","authors":"Akhlad Iqbal, Askar Hussain","doi":"10.3934/naco.2023010","DOIUrl":"https://doi.org/10.3934/naco.2023010","url":null,"abstract":"In this paper, we extend the class of strongly $E$-preinvex and strongly $E$-invex functions to quasi strongly $E$-preinvex, quasi strongly $E$-invex and pseudo strongly $E$-invex functions. Some nontrivial suitable examples have been constructed in support of our definitions. Several interesting properties and relationships of these functions are discussed. Furthermore, to show the application of our results, we consider a nonlinear programming problem and show that the local minimum point is also a strictly global minimum.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77226755","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}
{"title":"Going forward & backward with Jin Ma","authors":"P. Protter","doi":"10.3934/naco.2023005","DOIUrl":"https://doi.org/10.3934/naco.2023005","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78381824","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}
Abd El-Monem A. Megahed, Ebrahim A. Youness, Hebatallah K. Arafat
One of the most critical problems facing governments at present is terrorism. Most recent studies are striving to find an optimal solution to this problem that threatens the security and stability of people. To combat terrorism, government uses various means, such as improving education quality, providing labor opportunities, seeking social justice, creating religious awareness, and building security arrangements. This study aims to evaluate the optimum strategy for both government and terrorist organization using a min-max zero-sum differential game approach. In addition, it analyses the dynamics of the government's activities separately and explain the impact of the government's counter-terror measures on the activity and strength of international terror organization.
{"title":"Optimization method in counter terrorism: min-max zero-sum differential game approach","authors":"Abd El-Monem A. Megahed, Ebrahim A. Youness, Hebatallah K. Arafat","doi":"10.3934/naco.2022013","DOIUrl":"https://doi.org/10.3934/naco.2022013","url":null,"abstract":"One of the most critical problems facing governments at present is terrorism. Most recent studies are striving to find an optimal solution to this problem that threatens the security and stability of people. To combat terrorism, government uses various means, such as improving education quality, providing labor opportunities, seeking social justice, creating religious awareness, and building security arrangements. This study aims to evaluate the optimum strategy for both government and terrorist organization using a min-max zero-sum differential game approach. In addition, it analyses the dynamics of the government's activities separately and explain the impact of the government's counter-terror measures on the activity and strength of international terror organization.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","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":"136296833","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, we give several new results on solvability of a quadratic BSDE whose generator depends also on the mean of both variables. First, we consider such a BSDE using John-Nirenberg's inequality for BMO martingales to estimate its contribution to the evolution of the first unknown variable. Then we consider the BSDE having an additive expected value of a quadratic generator in addition to the usual quadratic one. In this case, we use a deterministic shift transformation to the first unknown variable, when the usual quadratic generator depends neither on the first variable nor its mean. The general case can be treated by a fixed point argument.
{"title":"Mean-field type quadratic BSDEs","authors":"Hélène Hibon, Ying Hu, Shanjian Tang","doi":"10.3934/naco.2022009","DOIUrl":"https://doi.org/10.3934/naco.2022009","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we give several new results on solvability of a quadratic BSDE whose generator depends also on the mean of both variables. First, we consider such a BSDE using John-Nirenberg's inequality for BMO martingales to estimate its contribution to the evolution of the first unknown variable. Then we consider the BSDE having an additive expected value of a quadratic generator in addition to the usual quadratic one. In this case, we use a deterministic shift transformation to the first unknown variable, when the usual quadratic generator depends neither on the first variable nor its mean. The general case can be treated by a fixed point argument.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","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":"136092720","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}
{"title":"Convergence analysis of multiple-sets split equality common fixed point problem with applications","authors":"N. Gupta, L. Jolaoso, Ashish Nandal, R. Chugh","doi":"10.3934/naco.2023012","DOIUrl":"https://doi.org/10.3934/naco.2023012","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82710392","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}
An orthonormal basis matrix $ X $ of a subspace $ {mathcal X} $ is known not to be unique, unless there are some kinds of normalization requirements. One of them is to require that $ X^{ text{T}}D $ is positive semi-definite, where $ D $ is a constant matrix of apt size. It is a natural one in multi-view subspace learning models in which $ X $ serves as a projection matrix and is determined by a maximization problem over the Stiefel manifold whose objective function contains and increases with $ text{tr}(X^{ text{T}}D) $. This paper is concerned with bounding the change in orthonormal basis matrix $ X $ as subspace $ {mathcal X} $ varies under the requirement that $ X^{ text{T}}D $ stays positive semi-definite. The results are useful in convergence analysis of the NEPv approach (nonlinear eigenvalue problem with eigenvector dependency) to solve the maximization problem.
已知子空间$ {mathcal X} $的标准正交基矩阵$ X $不是唯一的，除非有某种归一化要求。其中之一是要求$ X^{text{T}}D $是正半定的，其中$ D $是一个大小合适的常数矩阵。它是多视图子空间学习模型中的一个自然问题，其中$ X $作为投影矩阵，由Stiefel流形上的最大化问题决定，其目标函数包含$ text{tr}(X^{text{T}}D) $并随其增加。本文研究了在$ X^{text{T}}D $为正半定的条件下，当子空间${数学X} $变化时，正交基矩阵$ X $的变化边界。所得结果对NEPv方法(具有特征向量依赖的非线性特征值问题)的收敛性分析具有参考价值。
{"title":"Variations of orthonormal basis matrices of subspaces","authors":"Zhongming Teng, Ren-Cang Li","doi":"10.3934/naco.2023021","DOIUrl":"https://doi.org/10.3934/naco.2023021","url":null,"abstract":"An orthonormal basis matrix $ X $ of a subspace $ {mathcal X} $ is known not to be unique, unless there are some kinds of normalization requirements. One of them is to require that $ X^{ text{T}}D $ is positive semi-definite, where $ D $ is a constant matrix of apt size. It is a natural one in multi-view subspace learning models in which $ X $ serves as a projection matrix and is determined by a maximization problem over the Stiefel manifold whose objective function contains and increases with $ text{tr}(X^{ text{T}}D) $. This paper is concerned with bounding the change in orthonormal basis matrix $ X $ as subspace $ {mathcal X} $ varies under the requirement that $ X^{ text{T}}D $ stays positive semi-definite. The results are useful in convergence analysis of the NEPv approach (nonlinear eigenvalue problem with eigenvector dependency) to solve the maximization problem.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","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":"135440832","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}
{"title":"A brief discussion about a predator-prey model including disease in predators with the delay effect","authors":"Debashis Das, Sarbani Chakraborty","doi":"10.3934/naco.2023018","DOIUrl":"https://doi.org/10.3934/naco.2023018","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85566248","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}
{"title":"Superhedging problem under ratio constraint: BSDE approaches with Malliavin calculus","authors":"Mingyu Xu","doi":"10.3934/naco.2023007","DOIUrl":"https://doi.org/10.3934/naco.2023007","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78328151","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}
{"title":"On equilibrium multivalued problems in the general model with the Boolean-valued bifunction","authors":"Vo Viet Tri","doi":"10.3934/naco.2023020","DOIUrl":"https://doi.org/10.3934/naco.2023020","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86306127","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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