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Smoothing algorithms for complementarity problems over symmetric cones. (English) Zbl 1198.90373
The authors study a smoothing function in the context of symmetric cones and show that this function is coercive under some suitable conditions. Another objective of this paper is to extend two generic frameworks of smoothing algorithms to solve the complementarity problems over symmetric cones and to show the global convergence of the algorithms under suitable assumptions. The authors also provide a specific smoothing Newton algorithm which is globally and locally quadratically convergent under suitable assumptions. The theory of Euclidean Jordan algebras is a basic tool which is extensively used in the analysis. Some numerical results of a smoothing Newton algorithm for solving second-order cone complementarity problems are also reported.

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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