The primal-dual interior point algorithm implemented in SeDuMi [24] is described in [25]. The algorithm has an worst case bound, and treats initialization issues by means of the self-dual embedding technique of [28]. The iterative solutions are updated in a product form, which makes it possible to provide highly accurate solutions.

The algorithm terminates successfully if the norm of the residuals in
the optimality conditions, or the Farkas system with or
, are less than the parameter `pars.eps`. The default
value for `pars.eps` is `1E-9`.

**Remarks:**

- SeDuMi exploits sparsity in
solving the normal equations; this results in a benefit for problems
with a large number of small order matrix variables, such as the
*copositivity*-problems in the Dimacs set. - However, for problems that involve a huge matrix variable (without a block diagonal structure), the implementation is slow and consumes an excessive amount of memory.

Hans D. Mittelmann 2002-08-17