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http://dx.doi.org/10.14317/jami.2013.795

MERIT FUNCTIONS FOR MATRIX CONE COMPLEMENTARITY PROBLEMS  

Wang, Li (School of Science, Shenyang Aerospace University)
Liu, Yong-Jin (School of Science, Shenyang Aerospace University)
Jiang, Yong (School of Science, Shenyang Aerospace University)
Publication Information
Journal of applied mathematics & informatics / v.31, no.5_6, 2013 , pp. 795-812 More about this Journal
Abstract
The merit function arises from the development of the solution methods for the complementarity problems defined over the cone of non negative real vectors and has been well extended to the complementarity problems defined over the symmetric cones. In this paper, we focus on the extension of the merit functions including the gap function, the regularized gap function, the implicit Lagrangian and others to the complementarity problems defined over the nonsymmetric matrix cone. These theoretical results of this paper suggest new solution methods based on unconstrained and/or simply constrained methods to solve the matrix cone complementarity problems (MCCP).
Keywords
Matrix cone complementarity problem; merit function; gap function; regularized gap function; implicit Lagrangian;
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