# util-potentreduc: Potential reduction algorithm utility functions In GNE: Computation of Generalized Nash Equilibria

## Description

Functions for the potential reduction algorithm

## Usage

 ```1 2 3 4 5 6 7``` ```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.

See also `GNE.ceq`.