%% function [util,f,w,e] = TDMAweights_nonlin(B,rates)%% Arguments:% B - routing matrix% rates - rates of links in different slots%% Output:% util - optimal utility% f    - rates of flows% w    - weigths (durations) of slots% e    - e != 0 if error (see fmincon).%% Description:%% find weights that maximizes utility fairness% we have the following system:%% max 	sum u(f_i)% subj. 	B*f <= x% 			x = R * w%% that is B*f - R*w <= 0, or [B|-R]*[f/x] <= 0%% NOTE: Does not work well, since we use non-linear optimization.% To use a linear approximation instead, see TDMAweights.m%function [util,f,w,e] = TDMAweights_nonlin(B,rates)l = size(rates,1);m = size(rates,2);nf = size(B,2);w0 = [zeros(nf,1);ones(m,1)/m];Ae = [zeros(1,nf),ones(1,m)];be = 1;A = [B, -rates];A = [A;zeros(m,nf),diag(-ones(m,1))];b = zeros(l+m,1);lb = zeros(m+nf,1);ub = [];options = optimset;options.GradObj = 'on';options.Hessian = 'off';options.LargeScale = 'off';options.MaxFunEvals = 1e5;options.Display = 'off';[w,util,e] = fmincon(@maxrouting,w0,A,b,Ae,be,lb,ub,[],options,m,nf);f = w(1:nf);w = w(nf+1:nf+m);if e <= 0	% There was an error	C'	netsize	D'endutil = - util;