NIR: Nikaido Isoda Reformulation

Description

functions of the Nikaido Isoda Reformulation of the GNEP

Usage

gapNIR(x, y, dimx, obj, argobj, param=list(), echo=FALSE)
gradxgapNIR(x, y, dimx, grobj, arggrobj, param=list(), echo=FALSE)
gradygapNIR(x, y, dimx, grobj, arggrobj, param=list(), echo=FALSE)
fpNIR(x, dimx, obj, argobj, joint, argjoint,  
	grobj, arggrobj, jacjoint, argjacjoint, param=list(), 
	echo=FALSE, control=list(), yinit=NULL, optim.method="default")

Value

A vector for funSSR or a matrix for jacSSR.

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.
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.

Author

Christophe Dutang

Details

gapNIR computes the Nikaido Isoda function of the GNEP, while gradxgapNIR and gradygapNIR give its gradient with respect to \(x\) and \(y\). fpNIR computes the fixed-point function.

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.