VIR {GNE}

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.