A Predictor-corrector Path-following Algorithm for Symmetric Optimization Based on Darvay's Technique
نویسنده
چکیده
In this paper, we present a predictor-corrector path-following interior-point algorithm for symmetric cone optimization based on Darvay's technique. Each iteration of the algorithm contains a predictor step and a corrector step based on a modification of the Nesterov and Todd directions. Moreover, we show that the algorithm is well defined and that the obtained iteration bound is √ log , where is the rank of Euclidean Jordan algebra.
منابع مشابه
Symmetric Primal-dual Path following Algorithms for Semideenite Programming
In this paper a symmetric primal-dual transformation for positive semideenite 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 transformation is a well known fact. Based on this symmetric primal-dual transformation we derive Newt...
متن کاملCorrector-predictor arc-search interior-point algorithm for $P_*(kappa)$-LCP acting in a wide neighborhood of the central path
In this paper, we propose an arc-search corrector-predictor interior-point method for solving $P_*(kappa)$-linear complementarity problems. The proposed algorithm searches the optimizers along an ellipse that is an approximation of the central path. The algorithm generates a sequence of iterates in the wide neighborhood of central path introduced by Ai and Zhang. The algorithm does not de...
متن کاملSymmetric primal - dual path following
In this paper a symmetric primal-dual transformation for positive semideenite 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 transformation is a well known fact. Based on this symmetric primal-dual transformation we derive Newt...
متن کاملSuperlinear Convergence of a Symmetric Primal-Dual Path Following Algorithm for Semidefinite Programming
This paper establishes the superlinear convergence of a symmetric primal dual path following algorithm for semide nite programming under the assumptions that the semide nite pro gram has a strictly complementary primal dual optimal solution and that the size of the central path neighborhood tends to zero The interior point algorithm considered here closely resembles the Mizuno Todd Ye predictor...
متن کاملA Predictor-Corrector Path-Following Algorithm for Dual-Degenerate Parametric Optimization Problems
Most path-following algorithms for tracing a solution path of a parametric nonlinear optimization problem are only certifiably convergent under strong regularity assumptions about the problem functions, in particular, the linear independence of the constraint gradients at the solutions, which implies a unique multiplier solution for every nonlinear program. In this paper we propose and prove co...
متن کامل