further arguments to be passed to GNE.nseq,
GNE.ceq, GNE.fpeq or GNE.minpb.
NOT to the functions func1 and func2.
echo
a logical to get some traces of the benchmark computation.
control, control.outer, control.inner
a list with control
parameters to be passed to GNE.xxx function.
Details
Computing generalized Nash Equilibrium can be done in three different approaches.
(i) extended KKT system
It consists in solving the non smooth extended Karush-Kuhn-Tucker
(KKT) system Φ(z)=0. func1 is Phi and func2 is Jac Phi.
(ii) fixed point approach
It consists in solving equation y(x)=x. func1 is y and
func2 is ?
(iii) gap function minimization
It consists in minimizing a gap function min V(x).
func1 is V and func2 is Grad V.
Value
For GNE.bench.ceq and GNE.bench.nseq, a data.frame
is returned with columns:
method
the name of the method.
fctcall
the number of calls of the function.
jaccall
the number of calls of the Jacobian.
comptime
the computation time.
normFx
the norm of the merit function at the final iterate.
code
the exit code.
localmethods
the name of the local method.
globalmethods
the name of the globalization method.
x
the final iterate.
For GNE.bench.minpb, a data.frame
is returned with columns:
method
the name of the method.
minfncall.outer
the number of calls of the merit function.
grminfncall.outer
the number of calls of the
gradient of the merit function.
gapfncall.inner
the number of calls of the gap function.
grgapfncall.outer
the number of calls of the
gradient of the gap function.
comptime
the computation time.
normFx
the norm of the merit function at the final iterate.
code
the exit code.
x
the final iterate.
For GNE.bench.fpeq, a data.frame
is returned with columns:
method
the name of the method.
fpfncall.outer
the number of calls of the fixed-point function.
merfncall.outer
the number of calls of the merit function.
gapfncall.inner
the number of calls of the gap function.
grgapfncall.outer
the number of calls of the
gradient of the gap function.
comptime
the computation time.
normFx
the norm of the merit function at the final iterate.
code
the exit code.
x
the final iterate.
Author(s)
Christophe Dutang
References
F. Facchinei, A. Fischer & V. Piccialli (2009),
Generalized Nash equilibrium problems and Newton methods,
Math. Program.
A. von Heusinger (2009),
Numerical Methods for the Solution of the Generalized Nash Equilibrium Problem,
Ph. D. Thesis.
A. von Heusinger & J. Kanzow (2009),
Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions,
Comput Optim Appl .
See Also
See GNE.fpeq, GNE.minpb, GNE.ceq
and GNE.nseq for other approaches.