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# Numerical Approach  The general numerical method used by pycalphad to compute equilibrium is Newton-Raphson with the BFGS method used to update an approximate Hessian at each iteration. The general Gibbs energy minimization problem can be stated in the following way.  \[  \textrm{min } G_m(T, P, f^i, y^i_{s, j}) \textrm{ where } c_k (T, P, f^i, y^i_{s, j}) = 0  \]