What Is Optimization Toolbox?

Preconditioned Conjugate GradientsPreconditioned Conjugate GradientsA popular way to solve large symmetric positive definite systems of linearequations is the method of Preconditioned Conjugate Gradients(PCG). This iterative approach requires the ability to calculate matrix-vectorproducts of the form where is an arbitrary vector. The symmetricpositive definite matrix M is a preconditioner for H. Thatis, whereis a well-conditioned matrix or a matrix with clustered eigenvalues.AlgorithmOptimization Toolbox uses this PCG algorithm, which it refers to as AlgorithmPCG.% Initializationsr = -g; p = zeros(n,1);% Preconditionz = M\r; inner1 = r'*z; inner2 = 0; d = z;% Conjugate gradient iterationfor k = 1:kmaxif k > 1beta = inner1/inner2;d = z + beta*d;endw = H*d; denom = d'*w;if denom