What Is Optimization Toolbox?

fsolveYoucanformulateandsolvetheproblemasA = [ 3 11 -2; 1 1 -2; 1 -1 1];b = [ 7; 4; 19];x = A\bx =13.2188-2.34383.4375AlgorithmThe Gauss-Newton, Levenberg-Marquardt, and large-scale methodsare based on the nonlinear least-squares algorithms also used inlsqnonlin. Useone of these methods if the system may not have azero. The algorithm still returns a point where the residual is small.However, if the Jacobian of the system is singular, the algorithm mightconverge to a point that is not a solution of the system of equations (see“Limitations” on page 8-121 and “Diagnostics” on page 8-120 following).Large-Scale Optimizationfsolve, withtheLargeScale option set to 'on' with optimset, usesthe large-scale algorithm if possible. This algorithm is a subspace trustregion method and is based on the interior-reflective Newton methoddescribed in [1] and [2]. Each iteration involves the approximatesolution of a large linear system using the method of preconditionedconjugate gradients (PCG). See “Trust-Region Methods for NonlinearMinimization” on page 4-3 and “Preconditioned Conjugate Gradients”on page 4-7.Medium-Scale OptimizationBy defaultfsolve chooses the medium-scale algorithm and uses thetrust-region dogleg method. The algorithm is a variant of the Powell8-119