In this paper, the optimal variational generalized Nash equilibrium(v-GNE) seeking problem in merely monotone games with linearly coupled cost functions is investigated, in which the feasible strategy domain of each a...In this paper, the optimal variational generalized Nash equilibrium(v-GNE) seeking problem in merely monotone games with linearly coupled cost functions is investigated, in which the feasible strategy domain of each agent is coupled through an affine constraint. A distributed algorithm based on the hybrid steepest descent method is first proposed to seek the optimal v-GNE. Then, an accelerated algorithm with relaxation is proposed and analyzed, which has the potential to further improve the convergence speed to the optimal v-GNE. Some sufficient conditions in both algorithms are obtained to ensure the global convergence towards the optimal v-GNE. To illustrate the performance of the algorithms, numerical simulation is conducted based on a networked Nash-Cournot game with bounded market capacities.展开更多
We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the con...We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.展开更多
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
Neural Networks (NN) are the functional unit of Deep Learning and are known to mimic the behavior of the human brain to solve complex data-driven problems. Whenever we train our own neural networks, we need to take ca...Neural Networks (NN) are the functional unit of Deep Learning and are known to mimic the behavior of the human brain to solve complex data-driven problems. Whenever we train our own neural networks, we need to take care of something called the generalization of the neural network. The performance of Artificial Neural Networks (ANN) mostly depends upon its generalization capability. In this paper, we propose an innovative approach to enhance the generalization capability of artificial neural networks (ANN) using structural redundancy. A novel perspective on handling input data prototypes and their impact on the development of generalization, which could improve to ANN architectures accuracy and reliability is described.展开更多
Waveforms of seismic events,extracted from January 2019 to December 2021 were used to construct a test dataset to investigate the generalizability of PhaseNet in the Shandong region.The results show that errors in the...Waveforms of seismic events,extracted from January 2019 to December 2021 were used to construct a test dataset to investigate the generalizability of PhaseNet in the Shandong region.The results show that errors in the picking of seismic phases(P-and Swaves)had a broadly normal distribution,mainly concentrated in the ranges of−0.4–0.3 s and−0.4–0.8 s,respectively.These results were compared with those published in the original PhaseNet article and were found to be approximately 0.2–0.4 s larger.PhaseNet had a strong generalizability for P-and S-wave picking for epicentral distances of less than 120 km and 110 km,respectively.However,the phase recall rate decreased rapidly when these distances were exceeded.Furthermore,the generalizability of PhaseNet was essentially unaffected by magnitude.The M4.1 earthquake sequence in Changqing,Shandong province,China,that occurred on February 18,2020,was adopted as a case study.PhaseNet detected more than twice the number of earthquakes in the manually obtained catalog.This further verified that PhaseNet has strong generalizability in the Shandong region,and a high-precision earthquake catalog was constructed.According to these precise positioning results,two earthquake sequences occurred in the study area,and the southern cluster may have been triggered by the northern cluster.The focal mechanism solution,regional stress field,and the location results of the northern earthquake sequence indicated that the seismic force of the earthquake was consistent with the regional stress field.展开更多
In Orlicz-Bochner sequence spaces endowed with Orlicz norm and Luxemburg norm, points of lower monotonicity, upper monotonicity, lower local uniform monotonicity and upper local uniform monotonicity are characterized.
In this article,we propose a new algorithm and prove that the sequence generalized by the algorithm converges strongly to a common element of the set of fixed points for a quasi-pseudo-contractive mapping and a demi-c...In this article,we propose a new algorithm and prove that the sequence generalized by the algorithm converges strongly to a common element of the set of fixed points for a quasi-pseudo-contractive mapping and a demi-contraction mapping and the set of zeros of monotone inclusion problems on Hadamard manifolds.As applications,we use our results to study the minimization problems and equilibrium problems in Hadamard manifolds.展开更多
The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this ...The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].展开更多
A monotone iterative method for some discontinuous variational boundary problems is given, the convergence of iterative solutions is proved by the theory of partially ordered sets. It can be regarded as a generalizati...A monotone iterative method for some discontinuous variational boundary problems is given, the convergence of iterative solutions is proved by the theory of partially ordered sets. It can be regarded as a generalization of the classical monotone iteration theory for continuous problems.展开更多
Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate o...Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated.展开更多
In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly sm...In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.展开更多
The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied....The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.展开更多
Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differenti...Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differential equations in Banach spaces are studied. Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained.展开更多
In this paper, the existence of solutions for discontinuous nonlinear parabolic differential IBVP is proved by using a more generalized monotone iterative method. Moreover, the convergence of this method is discussed.
A proximal iterative algorithm for the mulitivalue operator equation 0 ∈ T(x) is presented, where T is a maximal monotone operator. It is an improvement of the proximal point algorithm as well know. The convergence o...A proximal iterative algorithm for the mulitivalue operator equation 0 ∈ T(x) is presented, where T is a maximal monotone operator. It is an improvement of the proximal point algorithm as well know. The convergence of the algorithm is discussed and all example is given.展开更多
The iterative solution for a class of multivalued monotone operator equations just like A(u)∈-B(u) is discussed, where A is a positive definite linear single valued operator, B is a bounded and m...The iterative solution for a class of multivalued monotone operator equations just like A(u)∈-B(u) is discussed, where A is a positive definite linear single valued operator, B is a bounded and monotone multivalued operator. The existence and convergence of approximate solutions are proved. The method of numerical realization is demonstrated in some examples.展开更多
Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space E and {An}n∈N be a family of monotone and Lipschitz continuos mappings of C into E＊. In this article, we consider th...Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space E and {An}n∈N be a family of monotone and Lipschitz continuos mappings of C into E＊. In this article, we consider the improved gradient method by the hybrid method in mathematical programming [i0] for solving the variational inequality problem for {AN} and prove strong convergence theorems. And we get several results which improve the well-known results in a real 2-uniformly convex and uniformly smooth Banach space and a real Hilbert space.展开更多
基金supported by the National Natural Science Foundation of China(Basic Science Center Program)(61988101)the Joint Fund of Ministry of Education for Equipment Pre-research (8091B022234)+3 种基金Shanghai International Science and Technology Cooperation Program (21550712400)Shanghai Pilot Program for Basic Research (22TQ1400100-3)the Fundamental Research Funds for the Central UniversitiesShanghai Artifcial Intelligence Laboratory。
文摘In this paper, the optimal variational generalized Nash equilibrium(v-GNE) seeking problem in merely monotone games with linearly coupled cost functions is investigated, in which the feasible strategy domain of each agent is coupled through an affine constraint. A distributed algorithm based on the hybrid steepest descent method is first proposed to seek the optimal v-GNE. Then, an accelerated algorithm with relaxation is proposed and analyzed, which has the potential to further improve the convergence speed to the optimal v-GNE. Some sufficient conditions in both algorithms are obtained to ensure the global convergence towards the optimal v-GNE. To illustrate the performance of the algorithms, numerical simulation is conducted based on a networked Nash-Cournot game with bounded market capacities.
基金supported by the NSFC(12071413)the Guangxi Natural Sci-ence Foundation(2023GXNSFAA026085)the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No.823731 CONMECH。
文摘We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
文摘Neural Networks (NN) are the functional unit of Deep Learning and are known to mimic the behavior of the human brain to solve complex data-driven problems. Whenever we train our own neural networks, we need to take care of something called the generalization of the neural network. The performance of Artificial Neural Networks (ANN) mostly depends upon its generalization capability. In this paper, we propose an innovative approach to enhance the generalization capability of artificial neural networks (ANN) using structural redundancy. A novel perspective on handling input data prototypes and their impact on the development of generalization, which could improve to ANN architectures accuracy and reliability is described.
基金funded by the General Scientific Research Project of the Shandong Earthquake Agency(No.YB2202)the National Key Research and Development Program Project(No.2021YFC3000700)a Key Project under the Natural Science Foundation of Shandong Province(No.ZR2020KF003).
文摘Waveforms of seismic events,extracted from January 2019 to December 2021 were used to construct a test dataset to investigate the generalizability of PhaseNet in the Shandong region.The results show that errors in the picking of seismic phases(P-and Swaves)had a broadly normal distribution,mainly concentrated in the ranges of−0.4–0.3 s and−0.4–0.8 s,respectively.These results were compared with those published in the original PhaseNet article and were found to be approximately 0.2–0.4 s larger.PhaseNet had a strong generalizability for P-and S-wave picking for epicentral distances of less than 120 km and 110 km,respectively.However,the phase recall rate decreased rapidly when these distances were exceeded.Furthermore,the generalizability of PhaseNet was essentially unaffected by magnitude.The M4.1 earthquake sequence in Changqing,Shandong province,China,that occurred on February 18,2020,was adopted as a case study.PhaseNet detected more than twice the number of earthquakes in the manually obtained catalog.This further verified that PhaseNet has strong generalizability in the Shandong region,and a high-precision earthquake catalog was constructed.According to these precise positioning results,two earthquake sequences occurred in the study area,and the southern cluster may have been triggered by the northern cluster.The focal mechanism solution,regional stress field,and the location results of the northern earthquake sequence indicated that the seismic force of the earthquake was consistent with the regional stress field.
文摘In Orlicz-Bochner sequence spaces endowed with Orlicz norm and Luxemburg norm, points of lower monotonicity, upper monotonicity, lower local uniform monotonicity and upper local uniform monotonicity are characterized.
基金This study was supported by the Natural Science Foundation of China Medical University,TaiwanThis work was also supported by Scientific Research Fund of SiChuan Provincial Education Department(14ZA0272).
文摘In this article,we propose a new algorithm and prove that the sequence generalized by the algorithm converges strongly to a common element of the set of fixed points for a quasi-pseudo-contractive mapping and a demi-contraction mapping and the set of zeros of monotone inclusion problems on Hadamard manifolds.As applications,we use our results to study the minimization problems and equilibrium problems in Hadamard manifolds.
基金Supported by National Natural Science Foundation of China
文摘The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].
文摘A monotone iterative method for some discontinuous variational boundary problems is given, the convergence of iterative solutions is proved by the theory of partially ordered sets. It can be regarded as a generalization of the classical monotone iteration theory for continuous problems.
文摘Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated.
基金the National Natural Science Foundation of China (10771050)
文摘In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.
基金Supported by the Natural Science Foundation of Zhejiang Province (Y605144)the XNF of Zhejiang University of Media and Communications (XN080012008034)
文摘The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.
文摘Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differential equations in Banach spaces are studied. Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained.
文摘In this paper, the existence of solutions for discontinuous nonlinear parabolic differential IBVP is proved by using a more generalized monotone iterative method. Moreover, the convergence of this method is discussed.
基金Supported by the National Natural Science Foundation of China
文摘A proximal iterative algorithm for the mulitivalue operator equation 0 ∈ T(x) is presented, where T is a maximal monotone operator. It is an improvement of the proximal point algorithm as well know. The convergence of the algorithm is discussed and all example is given.
文摘The iterative solution for a class of multivalued monotone operator equations just like A(u)∈-B(u) is discussed, where A is a positive definite linear single valued operator, B is a bounded and monotone multivalued operator. The existence and convergence of approximate solutions are proved. The method of numerical realization is demonstrated in some examples.
文摘Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space E and {An}n∈N be a family of monotone and Lipschitz continuos mappings of C into E＊. In this article, we consider the improved gradient method by the hybrid method in mathematical programming [i0] for solving the variational inequality problem for {AN} and prove strong convergence theorems. And we get several results which improve the well-known results in a real 2-uniformly convex and uniformly smooth Banach space and a real Hilbert space.
