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Weak and Strong Convergence of Self Adaptive Inertial Subgradient Extragradient Algorithms for Solving Variational Inequality Problems
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作者 Yao Li Hongwei Liu Jiamin Lv 《Journal of Harbin Institute of Technology(New Series)》 CAS 2024年第2期38-49,共12页
Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in th... Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in this paper.The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition.Two new algorithms adopt inertial technology and non-monotonic step size rule,and their convergence can still be proved when the value of L is not given in advance.Finally,some numerical results are designed to demonstrate the computational efficiency of our two new algorithms. 展开更多
关键词 variational inequality inertial method non-monotonic step size rule Lipschitz continuity pseudomonotone mapping
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Inertial Subgradient Extragradient Algorithm for Solving Variational Inequality Problems with Pseudomonotonicity
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作者 Yuwan Ding Hongwei Liu Xiaojun Ma 《Journal of Harbin Institute of Technology(New Series)》 CAS 2023年第5期65-75,共11页
In order to solve variational inequality problems of pseudomonotonicity and Lipschitz continuity in Hilbert spaces, an inertial subgradient extragradient algorithm is proposed by virtue of non-monotone stepsizes. More... In order to solve variational inequality problems of pseudomonotonicity and Lipschitz continuity in Hilbert spaces, an inertial subgradient extragradient algorithm is proposed by virtue of non-monotone stepsizes. Moreover, weak convergence and R-linear convergence analyses of the algorithm are constructed under appropriate assumptions. Finally, the efficiency of the proposed algorithm is demonstrated through numerical implementations. 展开更多
关键词 variational inequality extragradient method PSEUDOMONOTONICITY Lipschitz continuity weak and linear convergence
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A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES 被引量:1
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作者 Yunhua WENG Xuesong LI Nanjing HUANG 《Acta Mathematica Scientia》 SCIE CSCD 2021年第1期187-206,共20页
This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measur... This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established.By using a fixed point theorem for a condensing setvalued map,the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions.Finally,an example is presented to illustrate our main results. 展开更多
关键词 fractional differential variational inequality fractional nonlinear delay evolution equation hemi-variational inequality condensing map KKM theorem fixed point theorem
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QUASI-CONFORMING FINITE ELEMENT APPROXIMATION FOR A FOURTH ORDER VARIATIONAL INEQUALITY WITH DISPLACEMENT OBSTACLE 被引量:3
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作者 石东洋 陈绍春 《Acta Mathematica Scientia》 SCIE CSCD 2003年第1期61-66,共6页
In this paper, unconventional quasi-conforming finite element approximation for a fourth order variational inequality with displacement obstacle is considered, the optimal order of error estimate O(h) is obtained whic... In this paper, unconventional quasi-conforming finite element approximation for a fourth order variational inequality with displacement obstacle is considered, the optimal order of error estimate O(h) is obtained which is as same as that of the conventional finite elements. 展开更多
关键词 variational inequality unconventional quasi-conforming element optimal error estimate
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WEAK CONVERGENCE THEOREMS FOR GENERAL EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS IN BANACH SPACES 被引量:2
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作者 蔡钢 步尚金 《Acta Mathematica Scientia》 SCIE CSCD 2013年第1期303-320,共18页
In this paper, we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-stro... In this paper, we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces. Then we study the weak convergence of the two iterative sequences. Our results improve and extend the results announced by many others. 展开更多
关键词 weak convergence relatively nonexpansive mapping equilibrium problem variational inequality
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An FEM approximation for a fourth-order variational inequality of second kind 被引量:1
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作者 QIAN Fu-bin DING Rui 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第1期19-24,共6页
A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered. By using regularization method, the original problem can be formulated as a differentiable variatio... A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered. By using regularization method, the original problem can be formulated as a differentiable variational equation, and the corresponding discrete FEM variational equation is presented afterwards. Abstract error estimates and error estimates of the approximation are derived in terms of energy norm and L^2-norm. 展开更多
关键词 plate theory variational inequality of the second kind fourth-order problem FEM regularization error estimate.
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BOUNDARY MIXED VARIATIONAL INEQUALITYIN FRICTION PROBLEM 被引量:1
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作者 丁方允 张欣 丁睿 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第2期213-224,共12页
In this paper, with the use of the friction problem in elasticity as the background, the existence and uniqueness for the solution of the nonlinear, indifferentiable mixed variational inequality are discussed. Its cor... In this paper, with the use of the friction problem in elasticity as the background, the existence and uniqueness for the solution of the nonlinear, indifferentiable mixed variational inequality are discussed. Its corresponding boundary variational inequality and the existence and uniqueness, of solution are given. This provides the theoretical basis for using boundary element method to solve the mixed variational inequality. 展开更多
关键词 mixed variational inequality friction problem Sobolev space
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A Smoothing Newton Method for the Box Constrained Variational Inequality Problems 被引量:1
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作者 XIE Ya-jun MA Chang-feng 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第1期152-158,共7页
The box constrained variational inequality problem can be reformulated as a nonsmooth equation by using median operator.In this paper,we present a smoothing Newton method for solving the box constrained variational in... The box constrained variational inequality problem can be reformulated as a nonsmooth equation by using median operator.In this paper,we present a smoothing Newton method for solving the box constrained variational inequality problem based on a new smoothing approximation function.The proposed algorithm is proved to be well defined and convergent globally under weaker conditions. 展开更多
关键词 median operator variational inequality problem smoothing Newton method global convergence
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A predictor-corrector interior-point algorithmfor monotone variational inequality problems 被引量:2
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作者 梁昔明 钱积新 《Journal of Zhejiang University Science》 CSCD 2002年第3期321-325,共5页
Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work t... Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work the authors give a predictor corrector interior point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level 1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented. 展开更多
关键词 variational inequality problems(VIP) Predictor corrector interior point algorithm Numerical experiments
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RELAXED INERTIAL METHODS FOR SOLVING SPLIT VARIATIONAL INEQUALITY PROBLEMS WITHOUT PRODUCT SPACE FORMULATION 被引量:1
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作者 Grace Nnennaya OGWO Chinedu IZUCHUKWU Oluwatosin Temitope MEWOMO 《Acta Mathematica Scientia》 SCIE CSCD 2022年第5期1701-1733,共33页
Many methods have been proposed in the literature for solving the split variational inequality problem.Most of these methods either require that this problem is transformed into an equivalent variational inequality pr... Many methods have been proposed in the literature for solving the split variational inequality problem.Most of these methods either require that this problem is transformed into an equivalent variational inequality problem in a product space,or that the underlying operators are co-coercive.However,it has been discovered that such product space transformation may cause some potential difficulties during implementation and its approach may not fully exploit the attractive splitting nature of the split variational inequality problem.On the other hand,the co-coercive assumption of the underlying operators would preclude the potential applications of these methods.To avoid these setbacks,we propose two new relaxed inertial methods for solving the split variational inequality problem without any product space transformation,and for which the underlying operators are freed from the restrictive co-coercive assumption.The methods proposed,involve projections onto half-spaces only,and originate from an explicit discretization of a dynamical system,which combines both the inertial and relaxation techniques in order to achieve high convergence speed.Moreover,the sequence generated by these methods is shown to converge strongly to a minimum-norm solution of the problem in real Hilbert spaces.Furthermore,numerical implementations and comparisons are given to support our theoretical findings. 展开更多
关键词 split variational inequality problems relaxation technique inertial extrapolation minimum-norm solutions product space formulation half-spaces
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A NEW VARIATIONAL INEQUALITY FORMULATION FOR SEEPAGE PROBLEMS WITH FREE SURFACES
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作者 郑宏 刘德富 +1 位作者 李焯芬 谭国焕 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第3期396-406,共11页
A new variational inequality formulation for seepage problems with free surfaces was presented, in which a boundary condition of (Signorini's) type was prescribed over the potential seepage surfaces. This made the... A new variational inequality formulation for seepage problems with free surfaces was presented, in which a boundary condition of (Signorini's) type was prescribed over the potential seepage surfaces. This made the singularity of seepage points eliminated and the location of seepage points determined. Compared to other variational formulations, the proposed formulation owns better numerical stability. 展开更多
关键词 free boundary problem SEEPAGE variational inequality finite element
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THE VARIATIONAL INEQUALITY FORMULATION FOR THE DEFORMATION THEORY IN PLASTICITY AND ITS NON-ITERATIVE SOLUTION
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作者 郭小明 余颖禾 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1993年第12期1163-1172,共10页
In this paper, the deformation theory in plasticity is formulated in the variational inequality, which can relax the constraint conditions of the constitutive equations. The new form makes the calculation more conveni... In this paper, the deformation theory in plasticity is formulated in the variational inequality, which can relax the constraint conditions of the constitutive equations. The new form makes the calculation more convenient than general energy forms and have reliable mathematical basis. Thus the plasticity theory may be solved by means of the quadratic programming instead of the iterative methods. And the solutions can be made in one step without any diversion of the load. 展开更多
关键词 deformation theory in plasticity variational inequality quadratic programming
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A projected gradient method with nonmonotonic backtracking technique for solving convex constrained monotone variational inequality problem
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作者 WANG Yun-juan ZHU De-tong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第4期463-474,共12页
Based on a differentiable merit function proposed by Taji, et al in “Mathematical Programming, 1993, 58: 369-383”, a projected gradient trust region method for the monotone variational inequality problem with conve... Based on a differentiable merit function proposed by Taji, et al in “Mathematical Programming, 1993, 58: 369-383”, a projected gradient trust region method for the monotone variational inequality problem with convex constraints is presented. Theoretical analysis is given which proves that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm. 展开更多
关键词 trust region line search projected gradient variational inequality
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Existence and stability of solutions to inverse variational inequality problems
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作者 Yu HAN Nanjing HUANG +1 位作者 Jue LU Yibin XIAO 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2017年第5期749-764,共16页
In this paper, two new existence and quasi-variational inequality problems are theorems of solutions to inverse variational proved using the Fan-Knaster-Kuratowski- Mazurkiewicz (KKM) theorem and the Kakutani-Fan-Gl... In this paper, two new existence and quasi-variational inequality problems are theorems of solutions to inverse variational proved using the Fan-Knaster-Kuratowski- Mazurkiewicz (KKM) theorem and the Kakutani-Fan-Glicksberg fixed point theorem. Upper semicontinuity and lower semicontinuity of the solution mapping and the approximate solution mapping to the parametric inverse variational inequality problem are also discussed under some suitable conditions. An application to a road pricing problem is given. 展开更多
关键词 inverse variational inequality Fan-Knaster-Kuratowski-Mazurkiewicz (KKM)theorem Kakutani-Fan-Glicksberg fixed point theorem upper semicontinuity lower semicontinuity
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Convergence analysis on Browder-Tikhonov regularization for second-order evolution hemivariational inequality
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作者 Yibin XIAO Guoji TANG +1 位作者 Xianjun LONG Nanjing HUANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2015年第10期1371-1382,共12页
This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality (SOEHVI) with non-coercive operators. With duality mapping, the regularized formulations and a derived fi... This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality (SOEHVI) with non-coercive operators. With duality mapping, the regularized formulations and a derived first-order evolution hemivariational inequality (FOEHVI) for the problem considered are presented. By applying the Browder-Tikhonov regularization method to the derived FOEHVI, a sequence of regularized solutions to the regularized SOEHVI is constructed, and the strong convergence of the whole sequence of regularized solutions to a solution to the problem is proved. 展开更多
关键词 second-order evolution hemivariational inequality (SOEHVI) Browder-Tikhonov regularization Clarke's generalized gradient
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AN EXTRAGRADIENT METHOD FOR RELAXED COCOERCIVE VARIATIONAL INEQUALITY AND EQUILIBRIUM PROBLEMS
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作者 C.Jaiboon P.Kumam U.W.Humphries 《Analysis in Theory and Applications》 2009年第4期381-400,共20页
The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of ... The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of solutions of the variational inequality prob- lem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao[17], Takahashi[12] and many others. 展开更多
关键词 nonexpansive mapping relaxed cocoercive mapping variational inequality fixed point equilibrium problem extragradient method
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On Variational Inequality and Fixed Point Problems
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作者 LU Ai-xia WANG Qing-ling 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第2期208-212,共5页
In this paper,A strong convergence theorem for a finite family of nonexpansive mappings and relaxed cocoercive mappings based on an iterative method in the framework of Hilbert spaces is established.
关键词 CONTRACTION fixed point nonexpansive mapping variational inequality
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A NEW PROOF OF GAFFNEY’S INEQUALITY FOR DIFFERENTIAL FORMS ON MANIFOLDS-WITH-BOUNDARY:THE VARIATIONAL APPROACH à LA KOZONO-YANAGISAWA
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作者 Siran LI 《Acta Mathematica Scientia》 SCIE CSCD 2022年第4期1427-1452,共26页
Let(M,g_(0))be a compact Riemannian manifold-with-boundary.We present a new proof of the classical Gaffney inequality for differential forms in boundary value spaces over M,via a variational approach a la Kozono-Yanag... Let(M,g_(0))be a compact Riemannian manifold-with-boundary.We present a new proof of the classical Gaffney inequality for differential forms in boundary value spaces over M,via a variational approach a la Kozono-Yanagisawa[Lr-variational inequality for vector fields and the Helmholtz-Weyl decomposition in bounded domains,Indiana Univ.Math.J.58(2009),1853-1920],combined with global computations based on the Bochner technique. 展开更多
关键词 Gaffney’s inequality differential form Sobolev spaces on manifolds Bochner technique variational approach
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Modified Subgradient Extragradient Method for Variational Inequality Problems and Fixed Point Problems
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作者 Xiaoyin Li Hongwei Liu +1 位作者 Jiangli Cheng Dongyao Zhang 《Journal of Harbin Institute of Technology(New Series)》 CAS 2022年第5期11-19,共9页
Many approaches inquiring into variational inequality problems have been put forward,among which subgradient extragradient method is of great significance.A novel algorithm is presented in this article for resolving q... Many approaches inquiring into variational inequality problems have been put forward,among which subgradient extragradient method is of great significance.A novel algorithm is presented in this article for resolving quasi-nonexpansive fixed point problem and pseudomonotone variational inequality problem in a real Hilbert interspace.In order to decrease the execution time and quicken the velocity of convergence,the proposed algorithm adopts an inertial technology.Moreover,the algorithm is by virtue of a non-monotonic step size rule to acquire strong convergence theorem without estimating the value of Lipschitz constant.Finally,numerical results on some problems authenticate that the algorithm has preferable efficiency than other algorithms. 展开更多
关键词 inertial method fixed point variational inequality strong convergence subgradient extragradient method
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ON THE REGULARITY OF THE MINIMUM SOLUTION OF THE RESTRAINED VARIATIONAL PROBLEMS
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作者 沈尧天 郭信康 《Acta Mathematica Scientia》 SCIE CSCD 1993年第3期266-272,共7页
This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0... This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0(1,2) (Omega, R(N))\parallel to u parallel to L(D) = 1}. Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Holder continuous. 展开更多
关键词 HOLDER ON THE regularity OF THE MINIMUM SOLUTION OF THE RESTRAINED variational PROBLEMS
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