What Is Optimization Toolbox?

Large-Scale Exampleswere not the same size as H, fmincon would compute a preconditioner basedon some diagonal scaling matrices determined from the algorithm. Typically,this would not perform as well.Quadratic Minimization with Bound ConstraintsTo minimize a large-scale quadratic with upper and lower bounds, you canuse the quadprog function.The problem stored in the MAT-file qpbox1.mat is a positive definitequadratic, and the Hessian matrix H is tridiagonal, subject to upper (ub) andlower (lb) bounds.Step 1: Load the Hessian and define f, lb, and ub.load qpbox1 % Get Hlb = zeros(400,1); lb(400) = -inf;ub = 0.9*ones(400,1); ub(400) = inf;f = zeros(400,1); f([1 400]) = -2;Step 2: Call a quadratic minimization routine with a startingpoint xstart.xstart = 0.5*ones(400,1);[x,fval,exitflag,output] = ...quadprog(H,f,[],[],[],[],lb,ub,xstart);Looking at the resulting values of exitflag and output,exitflag =3output =iterations: 20algorithm: 'large-scale: reflective trust-region'firstorderopt: 9.6206e-006cgiterations: 1834message: [1x206 char]you can see that while convergence occurred in 20 iterations, the high numberof CG iterations indicates that the cost of the linear system solve is high. In2-65