functions of the Nikaido Isoda Reformulation of the GNEP
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")A vector for funSSR or a matrix for jacSSR.
a numeric vector.
a vector of dimension for x.
objective function (to be minimized), see details.
a list of additional arguments.
gradient of the objective function, see details.
a list of additional arguments of the objective gradient.
Hessian of the objective function, see details.
a list of additional arguments of the objective Hessian.
joint function, see details.
a list of additional arguments of the joint function.
gradient of the joint function, see details.
a list of additional arguments of the joint Jacobian.
a list of parameters.
a list with control parameters for the fixed point algorithm.
initial point when computing the fixed-point function.
optimization method when computing the fixed-point function.
a logical to show some traces.
Christophe Dutang
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.
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 GNE.fpeq.