New Approaches for Large Scale Semidefinite and Doubly Nonnegative Programs

Florian Jarre^*

A stable symmetrization of the linear systems arising in interior-point methods for solving linear and semidefinite programs is introduced. The symmetrization includes a novel pivoting strategy to minimize the norm of the right and side. As the search directions generated by the iterative solver will have fairly low relative accuracy, a new interior-point approach based on low accuracy search directions is presented and analyzed. In the numerical examples, this approach results in a surprisingly small number of outer iterations, indicating that the interior-point concept may also be suitable for ill-conditioned problems for which it is difficult to compute high accuracy search directions. An application with doubly nonnegative matrices concludes the talk.

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Plenary Lecture