R: Benchmark function

bench.GNE {GNE}

R Documentation

Benchmark function

Description

Benchmark function to compare GNE computational methods.

Usage

bench.GNE.nseq(xinit, ..., echo=FALSE, control=list())
bench.GNE.ceq(xinit, ..., echo=FALSE, control=list())
bench.GNE.fpeq(xinit, ..., echo=FALSE, control.outer=list(), 
	control.inner=list())
bench.GNE.minpb(xinit, ..., echo=FALSE, control.outer=list(), 
	control.inner=list())

Arguments

`xinit`	a numeric vector for the initial point.
`...`	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 \Phi(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 .