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2011•International Journal of Modern Physics BRequires access

MODIFIED PROJECTION METHOD FOR GENERAL VARIATIONAL INEQUALITIES

Abdellah Bnouhachem, Muhammad Aslam Noor, Zhaohan Sheng

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Abstract

In this paper, we suggest and analyze a modified descent-projection method for solving general variational inequalities. The method makes use of a descent direction to produce the new iterate and can be viewed as an improvement of the descent-projection method by using a new step size. We also prove the global convergence of the proposed method. An example is given to illustrate the efficiency and its comparison with other methods. Since the general variational inequalities include quasi variational inequalities and implicit complementarity problems as special cases, results proved in this paper continue to hold for these problems.

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What this paper is about

In this paper, we suggest and analyze a modified descent-projection method for solving general variational inequalities. The method makes use of a descent direction to produce the new iterate and can be viewed as an improvement of the descent-projection method by using a new step size. We also prove the global convergence of the proposed method. An example is given to illustrate the efficiency and its comparison with other methods. Since the general variational inequalities include quasi variational inequalities and implicit complementarity problems as special cases, results proved in this paper continue to hold for these problems.

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Available abstract

In this paper, we suggest and analyze a modified descent-projection method for solving general variational inequalities. The method makes use of a descent direction to produce the new iterate and can be viewed as an improvement of the descent-projection method by using a new step size. We also prove the global convergence of the proposed method. An example is given to illustrate the efficiency and its comparison with other methods. Since the general variational inequalities include quasi variational inequalities and implicit complementarity problems as special cases, results proved in this paper continue to hold for these problems.

Key concepts: Variational inequality, Convergence (economics), Complementarity (molecular biology), Descent (aeronautics), Projection (relational algebra), Projection method, Applied mathematics, Mathematical optimization

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