How good are the solvers and where can I find references to
algorithms used? Are there any benchmark tests available?
solvers grew up from an early version of the code PENNON. While the
original PENNON was a
typical academic software, whose primal
goal was to test and verify new algorithms, the main stress in
solvers is given to careful and efficient programming and robustness.
PENOPT solvers can solve all problems that the
original PENNON can, and
will always be equally fast or faster.
of benchmark tests for the original PENNON can be
The codes are or has been used by more than 70 users from both
the industry and academia.
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.
- M. Kocvara 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
Optimization, Kluwer Academic Publishers, Dordrecht, 2003,
- M. Kocvara and M. Stingl. PENNON - A Code for Convex
Programming. Optimization Methods and Software
- D. Henrion, M. Kocvara and M. Stingl.
Solving simultaneous stabilization BMI problems with PENNON.
LAAS-CNRS Research Report No. 03549, December 2003, LAAS Toulouse (ps).
- D. Henrion, J. Löfberg, M. Kocvara, M.
polynomial static output feedback problems
with PENBMI. LAAS-CNRS Research Report No. 05165, March 2005.
the joint IEEE Conference on Decision and Control and European Control
Conference, Sevilla, Spain, December 2005 (pdf).
- M. Kocvara and M. Stingl. On the solution of large-scale
problems by the modified barrier method using iterative solvers. Mathematical
Programming Series B, 109(2-3):413-444, 2007.
- M. Kocvara
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
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