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SOME NEW RESOLVENT METHODS FOR SOLVING GENERAL MIXED VARIATIONAL INEQUALITIES

ABDELLAH BNOUHACHEM

School of Management Science and Engineering, Nanjing University, Nanjing 210093, P. R. China

Ibn Zohr University, ENSA, BP 32/S, Agadir, Morocco

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MUHAMMAD ASLAM NOOR

Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan

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KHALIDA INAYAT NOOR

Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan

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, and

ZHAOHAN SHENG

School of Management Science and Engineering, Nanjing University, Nanjing 210093, P. R. China

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https://doi.org/10.1142/S021797921105936XCited by:1 (Source: Crossref)

Abstract

In this paper, we propose two methods for solving general mixed variational inequalities. In the first method, the new iterate is obtained by using a descent direction while the second method can be viewed as an extension of the first one by performing an additional projection step at each iteration and another optimal step length is employed to reach substantial progress in each iteration. It is proved theoretically that the lower-bound of the progress obtained by the second method is greater than that by the first one. Under certain conditions, the global convergence of the both methods is proved. The comparison of these methods with other methods for solving the mixed genera variational inequalities is an open interesting problem.

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