potential.reduction: 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)

Value

A numeric or a numeric vector.

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.

Author

Christophe Dutang

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.

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.