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Convergence of a smoothing algorithm for symmetric cone complementarity problems with a nonmonotone line search. (English) Zbl 1203.90123
Summary: We propose a smoothing algorithm for solving the monotone symmetric cone complementarity problems (SCCP for short) with a nonmonotone line search. We show that the nonmonotone algorithm is globally convergent under an assumption that the solution set of the problem concerned is nonempty. Such an assumption is weaker than those given in most existing algorithms for solving optimization problems over symmetric cones. We also prove that the solution obtained by the algorithm is a maximally complementary solution to the monotone SCCP under some assumptions.

90C25 Convex programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
Full Text: DOI
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