util-VIR: Nikaido Isoda Reformulation

In GNE: Computation of Generalized Nash Equilibria

Nikaido Isoda Reformulation

Description

functions of the Nikaido Isoda Reformulation of the GNEP

Usage

gapVIR(x, y, dimx, grobj, arggrobj, param=list(), echo=FALSE)
gradxgapVIR(x, y, dimx, grobj, arggrobj, heobj, argheobj, param=list(), echo=FALSE)
gradygapVIR(x, y, dimx, grobj, arggrobj, param=list(), echo=FALSE)
fpVIR(x, dimx, obj, argobj, joint, argjoint,  
	grobj, arggrobj, jacjoint, argjacjoint, param=list(), 
	echo=FALSE, control=list(), yinit=NULL, optim.method="default")

Arguments

x,y	a numeric vector.
dimx	a vector of dimension for x.
obj	objective function (to be minimized), see details.
argobj	a list of additional arguments.
grobj	gradient of the objective function, see details.
arggrobj	a list of additional arguments of the objective gradient.
heobj	Hessian of the objective function, see details.
argheobj	a list of additional arguments of the objective Hessian.
joint	joint function, see details.
argjoint	a list of additional arguments of the joint function.
jacjoint	gradient of the joint function, see details.
argjacjoint	a list of additional arguments of the joint Jacobian.
param	a list of parameters.
control	a list with control parameters for the fixed point algorithm.
yinit	initial point when computing the fixed-point function.
optim.method	optimization method when computing the fixed-point function.
echo	a logical to show some traces.

Details

gapVIR computes the Nikaido Isoda function of the GNEP, while gradxgapVIR and gradygapVIR give its gradient with respect to x and y. fpVIR computes the fixed-point function.

Value

A vector for funSSR or a matrix for jacSSR.

Author(s)

Christophe Dutang

References

A. von Heusinger & J. Kanzow (2009), Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions, Comput Optim Appl .

F. Facchinei, A. Fischer and V. Piccialli (2009), Generalized Nash equilibrium problems and Newton methods, Math. Program.

See Also

See also GNE.fpeq.

GNE documentation built on March 31, 2023, 9:25 p.m.