Inexact Solution of the Schur Complement Equation in a Primal - Dual Interior - Point Method for Semidefinite Programming
نویسنده
چکیده
منابع مشابه
An inexact interior point method for L 1-regularized sparse covariance selection
Sparse covariance selection problems can be formulated as log-determinant (log-det ) semidefinite programming (SDP) problems with large numbers of linear constraints. Standard primal-dual interior-point methods that are based on solving the Schur complement equation would encounter severe computational bottlenecks if they are applied to solve these SDPs. In this paper, we consider a customized ...
متن کاملCorrelative Sparsity in Primal-dual Interior-point Methods for Lp, Sdp and Socp B-434 Correlative Sparsity in Primal-dual Interior-point Methods for Lp, Sdp and Socp
Exploiting sparsity has been a key issue in solving large-scale optimization problems. The most time-consuming part of primal-dual interior-point methods for linear programs, secondorder cone programs, and semidefinite programs is solving the Schur complement equation at each iteration, usually by the Cholesky factorization. The computational efficiency is greatly affected by the sparsity of th...
متن کاملABS Solution of equations of second kind and application to the primal-dual interior point method for linear programming
Abstract We consider an application of the ABS procedure to the linear systems arising from the primal-dual interior point methods where Newton method is used to compute path to the solution. When approaching the solution the linear system, which has the form of normal equations of the second kind, becomes more and more ill conditioned. We show how the use of the Huang algorithm in the ABS cl...
متن کاملAn inexact dual logarithmic barrier method for solving sparse semidefinite programs
A dual logarithmic barrier method for solving large, sparse semidefinite programs is proposed in this paper. The method avoids any explicit use of the primal variable X and therefore is well-suited to problems with a sparse dual matrix S. It relies on inexact Newton steps in dual space which are computed by the conjugate gradient method applied to the Schur complement of the reduced KKT system....
متن کاملA path following interior-point algorithm for semidefinite optimization problem based on new kernel function
In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we sho...
متن کامل