Some iterative schemes for general mixed variational inequalities

Noor, Muhammad Aslam

doi:10.1007/s12190-009-0306-x

J. Appl. Math. Comput.

2009

DOI: 10.1007/s12190-009-0306-x

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Some iterative schemes for general mixed variational inequalities

Muhammad Aslam Noor

Abstract: In this paper, we consider a class of variational inequalities which is called the general mixed variational inequality. It is known that the general mixed variational inequalities are equivalent to the fixed point problems. This equivalent formulation is used to suggest and analyze some three-step iterative schemes for finding the common element of the set of fixed points of a nonexpansive mappings and the set of solutions of the mixed variational inequalities. We also study the convergence criteria of threes… Show more

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Cited by 3 publications

References 24 publications

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A projection iterative algorithm boundary element method for the Signorini problem

Zhang¹,

Zhu²

2013

Engineering Analysis with Boundary Elements

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We propose a projection iterative algorithm based on a fixed point equation for solving a certain class of Signorini problem. The satisfaction of the Signorini boundary conditions is verified in a projection iterative manner, and at each iterative step, an elliptic mixed boundary value problem is solved by a boundary element method which is suitable for any domain. We prove the convergence of the algorithm by the property of projection. The advantage of this algorithm is that it is easy to be implemented and converge quickly. Some numerical results show the accuracy and effectiveness of the algorithm.

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A projection iterative algorithm boundary element method for the Signorini problem

Zhang¹,

Zhu²

2013

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

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Mixed Variational Inequalities and Nonconvex Analysis

Noor,

Noor

2024

EJMS

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In this expository paper, we provide an account of fundamental aspects of mixed variational inequalities with major emphasis on the computational properties, various generalizations, dynamical systems, nonexpansive mappings, sensitivity analysis and their applications. Mixed variational inequalities can be viewed as novel extensions and generalizations of variational principles. A wide class of unrelated problems, which arise in various branches of pure and applied sciences are being investigated in the unified framework of mixed variational inequalities. It is well known that variational inequalities are equivalent to the fixed point problems. This equivalent fixed point formulation has played not only a crucial part in studying the qualitative behavior of complicated problems, but also provide us numerical techniques for finding the approximate solution of these problems. Our main focus is to suggest some new iterative methods for solving mixed variational inequalities and related optimization problems using resolvent methods, resolvent equations, splitting methods, auxiliary principle technique, self-adaptive method and dynamical systems coupled with finite difference technique. Convergence analysis of these methods is investigated under suitable conditions. Sensitivity analysis of the mixed variational inequalities is studied using the resolvent equations method. Iterative methods for solving some new classes of mixed variational inequalities are proposed and investigated. Our methods of discussing the results are simple ones as compared with other methods and techniques. Results proved in this paper can be viewed as significant and innovative refinement of the known results.

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Resolvent Dynamical Systems Technique for Mixed General Variational Inequalities

Noor,

Noor

2024

EJMS

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In this paper, we introduce new second order dynamical system approach for solving a class of mixed general variational inequalities. Using the forward finite difference schemes, we suggest some multi-step iterative methods for solving the mixed variational inequalities. Convergence analysis is investigated under certain mild conditions. Some special cases are discussed as applications of the results. It is an interesting problem to compare these methods with other technique for solving mixed variational inequalities and related optimizations.

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Some iterative schemes for general mixed variational inequalities

Cited by 3 publications

References 24 publications

A projection iterative algorithm boundary element method for the Signorini problem

A projection iterative algorithm boundary element method for the Signorini problem

Mixed Variational Inequalities and Nonconvex Analysis

Resolvent Dynamical Systems Technique for Mixed General Variational Inequalities

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