penalty
method for nonlinear
and semidefinite programming
PENNON
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 Lagrangian
method pioneered by R. Polyak.
Complete theory,
the full algorithm and results of extensive testing is available in the thesis of Michael Stingl "On
the Solution of Nonlinear Semidefinite Programs by Augmented Lagrangian
Methods".
NEW-
try PENLABa free open source MATLAB® toolbox for nonlinear optimization,
linear and nonlinear semidefinite optimization and any combination of these.
PENLAB
has been developed in collaboration with NAG.
linear SDP problems with
SDPA input data file solved by PENSDP.
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 also need to change some control parameters in the
file in.txt.
try
(on NEOS) the new release of PENSDP, using the conjugate-gradient
method and approximate Hessians. For certain problems, the speed-up
factor is almost 100, compared to the standard PENSDP. 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.
PENNON
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.
PENNON
is also employed as an optimization solver in the software package
MOPED for material and topology optimization of elastic structures.
Here it helps to solve real-world problems
of aircraft industry.
During the years, we have collected a number of test examples
(linear SDP), small to large scale, generally sparse. The corresponding
input files in SDPA format can be found here.
PENNON
is available
through PENOPT GbR; there you can also
find more details about the code. If you have any questions, please contact
Michal Kocvara or Michael
Stingl.
M. Kočvara and M. Stingl. PENNON - A Generalized Augmented Lagrangian
Method for Semidefinite Programming. In G. Di Pillo and A. Murli, eds.,
High Performance Algorithms and Software for Nonlinear Optimization,
Kluwer Academic Publishers, Dordrecht, 2003, pp. 297-315 (pdf).
M. Kočvara and M. Stingl. PENNON - A Code for Convex Nonlinear and
Semidefinite Programming. Optimization Methods and Software
18(3):317-333, 2003 (pdf)
D. Henrion, J. Löfberg, M. Kočvara, M. Stingl. Solving polynomial
static output feedback problems with PENBMI. Proceedings of
the 44th IEEE Conference on Decision and Control, and the European
Control Conference 2005, Seville, Spain, December 12-15, 2005, pp.
7581-7586 (pdf).
M. Kočvara and M. Stingl. PENNON: Software for Linear and Nonlinear
Matrix Inequalities. In:
Handbook on Semidefinite, Conic and Polynomial Optimization, Anjos,
Miguel F.; Lasserre, Jean B. (Eds.), Springer, 2012, pp. 755-794, ISBN 978-1-4614-0768-3
J. Fiala, M. Kočvara, and M. Stingl. PENLAB: A MATLAB solver for
nonlinear semidefinite optimization.arXiv:1311.5240
(2013).