The Codes

The submitted codes fall naturally into two major groups and several subgroups:

• The first major group is that of primal-dual interior point methods designed for small to medium sized problems.
  • In the first subgroup are the codes SeDuMi, and SDPT3. These codes handle all 3 types of cones. SDPT3 was enabled to handle second order cones during the course of the Challenge.
  • In the second subgroup are SDPA, and CSDP, which are limited to SDP.
  • In the third subgroup are codes not designed for SDP problems but for convex (MOSEK) and nonconvex as well as convex (LOQO) nonlinear optimization. In fact, late in the Challenge an SDP interface for LOQO was provided but it did not solve satisfactorily any of the Challenge problems and these results were not included below. LOQO did solve some smaller SDPLIB problems.
• The second group is that of large-scale SDP codes designed to provide approximate solutions for large scale problems: BMPR, BMZ, BUNDLE and DSDP. The first three of these do not make use of second order derivative information, while DSDP is a dual interior point code.

In the following the codes will be listed in the above order.

The input formats are:

graph: Graph format as provided by the organizers.

Matlab: SeDuMi format in Matlab binary form as provided by organizers.

QPS: extended MPS format as explained in the MOSEK user's guide [20]; this was generated from the Matlab format with a converter provided by E. Andersen.

SDPA: the sparse SDPA format as explained in the SDPA user's guide; problems not provided in this format were converted from Matlab format to SDP formulation with the help of a program provided by B. Borchers.