In this paper, 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 conv...In this paper, 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.展开更多
In this paper, we establish a theoretical framework of path-following interior point al- gorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P*(κ)-property, a weaker condi...In this paper, we establish a theoretical framework of path-following interior point al- gorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-, semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh to the Cartesian P*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 10571134, 10671010)Natural Science Foundation of Tianjin (Grant No. 07JCYBJC05200)
文摘In this paper, 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.
基金supported by National Natural Science Foundation of China (Grant Nos. 10671010, 70841008)
文摘In this paper, we establish a theoretical framework of path-following interior point al- gorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-, semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh to the Cartesian P*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms.
