PENNON is a commercial solver, but time-limited academic licenses can be obtained from http://www.penopt.com
PENNON is invoked with sdpsettings('solver','pennon').
PENNON is not accessible in the current version of YALMIP, but will be in a forthcoming release. If you need it now, ask for a beta release.
PENNON is used as a general purpose nonlinear solver, and in particular used as an upper bound solver when solving nonconvex problems using BMIBNB, or lower bound solver when solving mixed-integer problems using BNB.
PENNON can also be used by YALMIP to solve geometric programming problems. In these cases, YALMIP automatically performs the standard convexifying variable change and solves the convex problem instead. To explicitly tell YALMIP to try to perform this conversion, use the tag 'pennon-geometric'. To tell YALMIP not to try to find a geometric program, use 'pennon-standard'.
Please note that YALMIP currently lacks the possibility to supply PENNON with Hessian expressions, which causes the solver to run slower than would be possible otherwise.