This article deals with a class of variational inequalities known as absolute value variational inequalities. Some new merit functions for the absolute value variational inequalities are established. Using these merit functions, we derive the error bounds for absolute value variational inequalities. Since absolute value variational inequalities contain variational inequalities, absolute value complementarity problem and system of absolute value equations as special cases, the findings presented here recapture various known results in the related domains. The conclusions of this paper are more comprehensive and may provoke futuristic research.
Citation: Safeera Batool, Muhammad Aslam Noor, Khalida Inayat Noor. Merit functions for absolute value variational inequalities[J]. AIMS Mathematics, 2021, 6(11): 12133-12147. doi: 10.3934/math.2021704
This article deals with a class of variational inequalities known as absolute value variational inequalities. Some new merit functions for the absolute value variational inequalities are established. Using these merit functions, we derive the error bounds for absolute value variational inequalities. Since absolute value variational inequalities contain variational inequalities, absolute value complementarity problem and system of absolute value equations as special cases, the findings presented here recapture various known results in the related domains. The conclusions of this paper are more comprehensive and may provoke futuristic research.
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Safeera Batool, Muhammad Aslam Noor, Khalida Inayat Noor. Merit functions for absolute value variational inequalities[J]. AIMS Mathematics, 2021, 6(11): 12133-12147. doi: 10.3934/math.2021704
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