R: Potential reduction algorithm utility functions

potential.reduction {GNE}

R Documentation

Potential reduction algorithm utility functions

Description

Functions for the potential reduction algorithm

Usage


potential.ce(u, n, zeta)

gradpotential.ce(u, n, zeta)	

psi.ce(z, dimx, dimlam, Hfinal, argfun, zeta)

gradpsi.ce(z, dimx, dimlam, Hfinal, jacHfinal, argfun, argjac, zeta)

Arguments

`u`	a numeric vector : `u=(u_1, u_2)` where `u_1` is of size `n`.
`n`	a numeric for the size of `u_1`.
`zeta`	a positive parameter.
`z`	a numeric vector : `z=(x, lambda, w)` where `dimx` is the size of components of `x` and `dimlam` is the size of components of `lambda` and `w`.
`dimx`	a numeric vector with the size of each components of `x`.
`dimlam`	a numeric vector with the size of each components of `lambda`. We must have `length(dimx) == length(dimlam)`.
`Hfinal`	the root function.
`argfun`	a list of additionnals arguments for `Hfinal`.
`jacHfinal`	the Jacobian of the root function.
`argjac`	a list of additionnals arguments for `jacHfinal`.

Details

potential.ce is the potential function for the GNEP, and gradpotential.ce its gradient. psi.ce is the application of the potential function for Hfinal, and gradpsi.ce its gradient.

Value

A numeric or a numeric vector.

Author(s)

Christophe Dutang

References

S. Bellavia, M. Macconi, B. Morini (2003), An affine scaling trust-region approach to bound-constrained nonlinear systems, Applied Numerical Mathematics 44, 257-280

A. Dreves, F. Facchinei, C. Kanzow and S. Sagratella (2011), On the solutions of the KKT conditions of generalized Nash equilibrium problems, SIAM Journal on Optimization 21(3), 1082-1108.