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Global and global linear convergence of smoothing algorithm for the Cartesian $P_*(\kappa)$-SCLCP

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  • In this paper, we consider the linear complementarity problem over Euclidean Jordan algebras with a Cartesian $P_*(\kappa)$-transformation, which is denoted by the Cartesian $P_*(\kappa)$-SCLCP. A smoothing algorithm is extended to solve the Cartesian $P_*(\kappa)$-SCLCP. We show that the algorithm is globally convergent if the problem concerned has a solution. In particular, we show that the algorithm is globally linearly convergent under a weak assumption.
    Mathematics Subject Classification: Primary: 90C22, 90C25; Secondary: 90C33.


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