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A Posteriori Parameter Choice Strategy for Nonlinear monotone operator Equations

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Acta Mathematicae Applicatae Sinica 2002年第2期18卷 289-294页

作者： Hong-qi Yang, Zong-yi HouDepartment of Scientific Computing & Computer Applications, Zhongshan University, Guangzhou 510275,ChinaDepartment of Mathematics, Pudan University, Shanghai 200433, China Department of Scientific Computing & Computer Applications Zhongshan University Guangzhou China Department of Mathematics Fudan University Shanghai China

In this paper we present an a posteriori parameter choice strategy for nonlinear ill-posed operator equations involving monotone operators. Under certain conditions, this a posteriori parameter choice strategy guarantees the optimal convergence rate O (δ1/2) for Tikhonov-Browder regularization, where δ denotes the noise level of the data perturbation.

关键词： Nonlinear operator equation monotone operator convergence rate a posteriori parameter choice

The Iterative Solution for a Class of monotone operator Equations

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Wuhan University Journal of Natural Sciences 1999年第2期4卷 24-26页

作者： Xiao Jin-sheng Lei Jin-gan

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.

关键词： multivalued operator monotone operator iterative solution

Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition

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Communications in Computational Physics 2023年第2期33卷 568-595页

作者： Mingze Qin Ruishu Wang Qilong Zhai Ran Zhang School of Mathematics Jilin UniversityChangchun 130012P.R.China.

The weak Galerkin(WG)method is a nonconforming numerical method for solving partial differential equations.In this paper,we introduce the WG method for elliptic equations with Newton boundary condition in bounded domains.The Newton boundary condition is a nonlinear boundary condition arising from science and engineering applications.We prove the well-posedness of the WG scheme by the monotone operator theory and the embedding inequality of weak finite element functions.The error estimates are derived.Numerical experiments are presented to verify the theoretical analysis.

关键词： Weak Galerkin method Newton boundary condition monotone operator embedding theorem.

DIFFERENTIAL VARIATIONAL INEQUALITIES IN INFINITE BANACH SPACES

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Acta Mathematica Scientia 2017年第1期37卷 26-32页

作者：刘振海曾生达 Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation and College of SciencesGuangxi University for Nationalities Institute of Computer Science Faculty of Mathematics and Computer Science Jagiellonian University

In this paper,we consider a new differential variational inequality（DVI,for short）which is composed of an evolution equation and a variational inequality in infinite Banach spaces.This kind of problems may be regarded as a special feedback control problem.Based on the Browder＇s theorem and the optimal control theory,we show the existence of solutions to the mentioned problem.

关键词： differential variational inequality C0-semigroup monotone operator existcnceof solutions

The monotone Method for Controllability of the Nonlinear Evolution Systems

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Acta Mathematicae Applicatae Sinica 2011年第4期27卷 721-726页

作者： Yue LU Yong LI Ming-ji LIU College of Mathematics Jilin University Changchun 130012 China

In this paper, we study the controllability of the nonlinear evolution systems. We establish the controllability results by using the monotone operator theory. No compactness assumptions are imposed in the main result... 详细信息

关键词： controllability monotone operator nonlinear control systems

Exact Controllability for a Class of Nonlinear Evolution Control Systems

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Communications in Mathematical Research 2015年第3期31卷 285-288页

作者： L Yue Li Yong College of Mathematics Jilin University

In this paper, we study the exact controllability of the nonlinear controlsystems. The controllability results by using the monotone operator theory are es-tablished. No compactness assumptions are imposed in the main... 详细信息

关键词： controllability monotone operator nonlinear evolution system coer-civity condition

Global Exponential Periodicity of a Class of Recurrent Neural Networks with Non-monotone Activation Functions and Time-Varying Delays

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Wuhan University Journal of Natural Sciences 2009年第6期14卷 475-480页

作者： LI Biwen School of Mathematics and Statistics Hubei Normal UniversityHuangshi 435002 Hubei China

The stability of a periodic oscillation and the global exponential class of recurrent neural networks with non-monotone activation functions and time-varying delays are analyzed. For two sets of activation functions, some algebraic criteria for ascertaining global exponential periodicity and global exponential stability of the class of recurrent neural networks are derived by using the comparison principle and the theory of monotone operator. These conditions are easy to check in terms of system parameters. In addition, we provide a new and efficacious method for the qualitative analysis of various neural networks.

关键词： recurrent neural networks non-monotone activation functions global exponential stability comparison principle monotone operator

A Relation between Resolvents of Subdifferentials and Metric Projections to Level Sets

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Applied Mathematics 2023年第6期14卷 428-435页

作者： Hiroko Okochi Faculty of Pharmacy Tokyo University of Pharmacy Tokyo Japan

An equation concerning with the subdifferential of convex functionals defined in real Banach spaces and the metric projections to level sets is shown. The equation is compared with the resolvents of general monotone operators, and makes the geometric properties of differential equations expressed by subdifferentials clear. Hence, it can be expected to be useful in obtaining the steepest descents defined by the convex functionals in Banach spaces. Also, it gives a similar result to the Lagrange multiplier method under certain conditions.

关键词： Subdifferential Convex Functional monotone operator Resolvent Lagrange Multiplier Banach Space Metric Projection

Regularization Methods to Approximate Solutions of Variational Inequalities

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Open Journal of Optimization 2023年第2期12卷 34-60页

作者： Nguyen Van Kinh Faculty of Applied Science Ho Chi Minh City University of Food Industry Ho Chi Minh City Vietnam

In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y0, A), we only know its approximate data satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones.

关键词： Ill-Posed Problem Variational Inequality Regularization Method monotone operator Hemi-Continuous operator Lower Semi-Continuous Function