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The relaxation modulus-based matrix splitting iteration methods for circular cone nonlinear complementarity problems. (English) Zbl 1413.90287

Summary: In this paper, we study a class of nonlinear complementarity problems associated with circular cone (CCNCP for short), which is a type of non-symmetric cone complementarity problems. Useful properties of the circular cone are investigated, which help to reformulate equivalently CCNCP as an implicit fixed-point equation. Based on the implicit fixed-point equation and splittings of the system matrix, we establish a class of relaxation modulus-based matrix splitting iteration methods for solving such a complementarity problem. The convergence of the proposed modulus-based matrix splitting iteration methods has been analyzed and the strategy choice of the parameters are discussed when the splitting matrix is symmetric positive definite. Numerical experiments have shown that the modulus-based iteration methods are effective for solving CCNCP.

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
65H10 Numerical computation of solutions to systems of equations

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