题目：On solving large scale semidefnite programs

报告人：Prof. FlorianJarre， University Dusseldorf

报告时间：2017年7月5日(周三) 10:00

报告地点：行健楼学术报告室526

邀请人：韩德仁教授

摘要：

This talk addresses the linear systems arising in interior point methods for linear and for semidefnite systems paying particular attention to systematic ill-conditioning. A stable symmetrization of the linear systems arising in interior-point methods for solving linear programs is introduced. A comparison of the condition numbers of the resulting interior-point linear systems with other commonly used approaches indicates that the new approach may be best suitable for an iterative solution. It is shown that there is a natural generalization of this symmetrization to the NT search direction for solving semidefnite programs. The generalization includes a novel pivoting strategy to minimize the norm of the right and side and heavily relies on the symmetry properties of the NT direction. The search directions generated by iterative solvers typically have fairly low relative accuracy. Nevertheless, in some preliminary numerical examples, a suitably adapted interior point approach results in a rather small number of outer iterations.