This page provides benchmarks of SDPpack Version 0.8 BETA on some randomly generated test problems, a set of 16 LMI problems (provided to us by P. Gahinet) from control applications, and a set of 8 problems (provided to us by A. Nemirovskii) from truss topology design. The LMI and the truss design problems are available as mat files from the SDPpack home page.

The truss design problems were solved with sdp.m with the default values of parameters set using setpars.m.

The LMI problems were solved with the same parameter settings, but with scalefac = 1000.

The benchmarks were conducted on an SGI workstation with a MIPS R10000 processor, a MIPS R10010 floating point unit and 192 MB of main memory, with Matlab 4.2c.1. In the tables, pinfeas, dinfeas and dgap are shown on a log scale (). Each * next to termflag indicates a restart.

Table: Randomly generated problems: (1) SDP with blk = [20 20] and m=40 solved with XZ+ZX, (2) diagonally constrained SDP with n = 20 solved with XZ, (3) same problem as in (2) solved with XZ+ZX, (4) Lovász function with n=10 and solved with XZ, and (5) same problem as in (4) solved with XZ+ZX.

Table: Randomly generated problems: (1) SDP with blk = [40 40] and m=80 solved with XZ+ZX, (2) diagonally constrained SDP with n = 40 solved with XZ, (3) same problem as in (2) solved with XZ+ZX, (4) Lovász function with n=20 and solved with XZ, and (5) same problem as in (4) solved with XZ+ZX.

Table: Randomly generated problems: (1) SDP with blk = [60 60] and m=120 solved with XZ+ZX, (2) diagonally constrained SDP with n = 60 solved with XZ, (3) same problem as in (2) solved with XZ+ZX, (4) Lovász function with n=30 and solved with XZ, and (5) same problem as in (4) solved with XZ+ZX.

Table: Benchmarks on LMI problems from control applications

Table: Benchmarks on problems from truss topology design