In this paper we consider properties of the central path and the analytic center of the optimalface in the context of parametric linear programming. We first show that if the right-hand sidevector of a standard linear program is perturbed, then the analytic center of the optimal face isone-side...

In this paper we consider properties of the central path and the analytic center of the optimalface in the context of parametric linear programming. We first show that if the right-hand sidevector of a standard linear program is perturbed, then the analytic center of the optimal face isone-side...

In this paper we consider properties of the central path and the analytic center of the optimal face in the context of parametric linear programming. We first show that if the right-hand side vector of a standard linear program is perturbed, then the analytic center of the optimal face is...

In this paper a symmetric primal-dual transformation for positive semidefinite programming is proposed. For standard SDP problems, after this symmetric transformation the primal variables and the dual slacks become identical. In the context of linear programming, existence of such a primal-dual...

In this paper we generalize the primal--dual cone affine scaling algorithm of Sturm and Zhang to semidefinite programming. We show in this paper that the underlying ideas of the cone affine scaling algorithm can be naturely applied to semidefinite programming, resulting in a new algorithm....

In this paper, we generalize the notion of weighted centers to semidefinite programming. Our analysis fits in the v-space framework, which is purely based on the symmetric primal-dual transformation and does not make use of barriers. Existence and scale invariance properties are proven for the...

It has been shown in various recent research reports that the analysis of short step primal-dual path following algorithms for linear programming can be nicely generalized to semidefinite programming. However, the analysis of long step path-following algorithms for semidefinite programming...

We propose in this paper an algorithm for solving linearly constrained nondifferentiable convex programming problems. This algorithm combines the ideas of the affine scaling method with the subgradient method. It is a generalization of the dual and interior point method for min-max problems...

We propose a polynomial time primal-dual potential reduction algorithm for linear programming. Unlike any other interior point method, the new algorithm is based on a rank-one updating scheme for sequentially computing the projection matrices. For a standard linear programming problem, the...