penalty method for
is a computer program for solving problems of convex and nonconvex
nonlinear programming and (generally nonlinear) semidefinite
programming. Originally an implementation of the PBM method of Ben-Tal
and Zibulevsky for problems of structural optimization, it has grown
into a stand alone program for solving general problems. PENNON
is particularly aimed at large-scale problems
with sparse data structure. It is based on a generalized augmented
The algorithm, implementation issues, and results of numerical tests
for linear SDP and SOCP problems can be found in a paper (pdf , ps) presented at
the workshop on High Performance Algorithms for Nonlinear Optimization,
In a newerreport (pdf , ps), published in a
final form in Optimization Methods and Software 18(3):317-333,
you will find more about the unified approach to NLP and SDP problems;
this paper also includes results of extensive tests.
NEW - complete theory, full algorithm and results of extensive testing now available in the thesis of Michael Stingl "On the Solution of Nonlinear Semidefinite Programs by Augmented Lagrangian Methods". The thesis, submitted in August 2005, is available here.
linear SDP problems with SDPA input data file.
To solve a problem
on the NEOS server, it is worth to read the README
file, in particular the comment on dense vs. sparse problems. You may
need to change some control parameters in the file
NEOS) the beta-version of the new release of PENNON, using the
conjugate-gradient method and approximate Hessians. For certain
problems, the speed-up factor is almost 100, compared to the standard
PENNON. Just choose your parameters in the file in.txt
general NLP problems with AMPL interface. Before
trying, you may read User's Guide
that also explains various options
for this version of the code.
and other codes: Hans
Mittelmann tested both versions, SDP and NLP, on a large set of
problems and compared several solvers, both academic and commercial.
Some of these test results in
the form of tables and
performance profiles can be also found here.
is also employed as an optimization solver in the software package MOPED for material and topology
optimization of elastic structures. Here it helps to sove real-world problems of aircraft industry.
Our main goal is to solve problems from structural optimization. We
collected several test examples
(linear SDP), small to large scale, generally sparse. The corresponding
input files in SDPA format can be found here.