What Is Optimization Toolbox?

lsqnonlinfor(that is, F should have k components).First, write an M-file to compute the k-component vector F.function F = myfun(x)k = 1:10;F = 2 + 2*k-exp(k*x(1))-exp(k*x(2));Next, invoke an optimization routine.x0 = [0.3 0.4][x,resnorm] = lsqnonlin(@myfun,x0)% Starting guess% Invoke optimizerAfter about 24 function evaluations, this example gives the solutionx =0.2578 0.2578resnorm % Residual or sum of squaresresnorm =124.3622AlgorithmLarge-Scale OptimizationBy default lsqnonlin chooses the large-scale algorithm. This algorithmis a subspace trust region method and is based on the interior-reflectiveNewton method described in [1] and [2]. Each iteration involves theapproximate solution of a large linear system using the method ofpreconditioned conjugate gradients (PCG). See “Trust-Region Methodsfor Nonlinear Minimization” on page 4-3 and “Preconditioned ConjugateGradients” on page 4-7.Medium-Scale OptimizationIf you set the LargeScale option set to 'off' with optimset, lsqnonlinuses the Levenberg-Marquardt method with line search [4], [5],and [6]. Alternatively, you can select a Gauss-Newton method [6]with line search by setting the LevenbergMarquardt option. SettingLevenbergMarquardt to 'off' (and LargeScale to 'off') selects the8-175