Functions for the potential reduction algorithm
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)
A numeric or a numeric vector.
a numeric vector : \(u=(u_1, u_2)\)
where \(u_1\) is of size n
.
a numeric for the size of \(u_1\).
a positive parameter.
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 \(w\).
a numeric vector with the size of each components of \(x\).
a numeric vector with the size of each components of \(lambda\).
We must have length(dimx) == length(dimlam)
.
the root function.
a list of additionnals arguments for Hfinal
.
the Jacobian of the root function.
a list of additionnals arguments for jacHfinal
.
Christophe Dutang
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.
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
.