<b><font> PENNON</font></b> test results

PENNON and other codes

The following results were collected from papers on PENNON and Hans Mittelmann's benchmark page. Some of them were not published yet.

Linear semidefinite programming

SDPLIB collection: table and performance profile
mater problems (large sparse SDP)
truss and shape problems (large sparse SDP - yet not as sparse as mater)

Convex programming
- Convex QP problems: performance profiles
Nonlinear programming
- AMPL-NLP problems: performance profiles

- The Higher The Better -

Performance profile (as introduced by Dolan and Moré; see also GAMS Performance World) measures performance of solvers (two and more) on a set P of problems. Assuming that t_p,s is a computing time required to solve problem p by solver s, one introduces a performance ratio as r_p,s = t_p,s / min{t_p,s : for all solvers s}. The performance profile (n_p is the number of problems)

rho_s(tau) = (1/n_p) size{p in P : r_p,s <= tau}

is the probability that a performance ratio r_p,sis within a factor tau of the best possible ratio. For instance, for tau = 2, rho_s(tau) says how often can solver s get results in a time not worse that two-times the time of the best solver. Also, the higher rho_s, the higher is the probability that solver s can solve all problems from P.

Michal Kocvara
June 30, 2003