What Is Optimization Toolbox?

2 Tutorial[fval,exitflag,output] = runqpbox4precto run the preceding code. After 18 iterations and 50 PCG iterations, thefunctionvaluehasthesamevaluetofivesignificantdigitsfval =-1.0538e+003but the first-order optimality is further reduced.output.firstorderopt =0.0028Note Decreasing TolPcg too much can substantially increase the number ofPCG iterations.Linear Least-Squares with Bound ConstraintsMany situations give rise to sparse linear least-squares problems, often withbounds on the variables. The next problem requires that the variables benonnegative. This problem comes from fitting a function approximation to apiecewise linear spline. Specifically, particles are scattered on the unit square.The function to be approximated is evaluated at these points, and a piecewiselinear spline approximation is constructed under the condition that (linear)coefficients are not negative. There are 2000 equations to fit on 400 variables:load particle % Get C, dlb = zeros(400,1);[x,resnorm,residual,exitflag,output] = ...lsqlin(C,d,[],[],[],[],lb);The default diagonal preconditioning works fairly well:exitflag =3resnorm =22.5794output =iterations: 102-72