On the basis of primal-dual approach, we present in this paper an interior point method that gives parametric E-approximate solutions to parametric semi-definite programming problems. The method is finite, and the num...On the basis of primal-dual approach, we present in this paper an interior point method that gives parametric E-approximate solutions to parametric semi-definite programming problems. The method is finite, and the number of its iterations is quasi-polynomially bounded.展开更多
Many problems in mathematical programming can be modelled as semidefinite programming. The success of interior point algorithms for large-scale linear programming has prompted researchers to develop these algorithms t...Many problems in mathematical programming can be modelled as semidefinite programming. The success of interior point algorithms for large-scale linear programming has prompted researchers to develop these algorithms to the semidefinite programming (SDP) case. In this paper, we extend Roos’s projective method for linear programming to SDP. The method is path-following and based on the useof a multiplicative barrier function. The iteration bound depends on the choice ofthe exponent μ in the numerator of the barrier function. The analysis in this paper resembles the one of the approximate center method for linear programming, as proposed by Rocs and Vial [14].展开更多
基金the National Natural Science Foundation of China!19871016
文摘On the basis of primal-dual approach, we present in this paper an interior point method that gives parametric E-approximate solutions to parametric semi-definite programming problems. The method is finite, and the number of its iterations is quasi-polynomially bounded.
文摘Many problems in mathematical programming can be modelled as semidefinite programming. The success of interior point algorithms for large-scale linear programming has prompted researchers to develop these algorithms to the semidefinite programming (SDP) case. In this paper, we extend Roos’s projective method for linear programming to SDP. The method is path-following and based on the useof a multiplicative barrier function. The iteration bound depends on the choice ofthe exponent μ in the numerator of the barrier function. The analysis in this paper resembles the one of the approximate center method for linear programming, as proposed by Rocs and Vial [14].
