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 study the properties of the analytic central path of asemidefinite programming problem under perturbation of a set of inputparameters. Specifically, we analyze the behavior of solutions on the centralpath with respect to changes on the right hand side of the...

In this paper we study the properties of the analytic central path of asemidefinite programming problem under perturbation of a set of inputparameters. Specifically, we analyze the behavior of solutions on the centralpath with respect to changes on the right hand side of the...

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...