biGls - Bilevel optimisation function using a global linear search
This function solves numerically the optimal network pricing problem given by: Max_y f(x(y),y)=y'x(y), subject to x being solution of the parametric (with parameter y) traffic assignment problem over the traffic network describe in the global variable %net.
The algorithm is based on a cyclic decomposition along coordenate axis of upper level objective function (given by the links prices y). In each direction a one-dimensional global optimization is performed using as initial point the optimum found in the previous iteration.
In this case GLSsci is used to do one-dimensional search. GLSsci is the Scilab version of Matlab GLS, Global Line Search. GLS is a Matlab program for univariate local or global optimization using function values only, implemented as optimization in R^n along a ray x+alp*p (alp>=0). Source of matlab version: http://www.mat.univie.ac.at/~neum/software/ls/
%net=TrafficExample("Steenbrink"); // uses the example net Steenbrink [prix,opfV,sfV,sP]=biGls([10,21],0,10,1,[0,0],1e-5);