Chemical equilibrium problem

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The problem is

\min \left\{ c^Tx + \sum_j \left(x_j \ln(x_j) \right) : x > 0, \; \sum\limits_j x_j = M, \; Ax=b \right\},
where the objective is the Gibbs free energy function with LaTeX: x_j being the number of moles of species LaTeX: j, LaTeX: b_i being the atomic weight of atom of type LaTeX: i, and LaTeX: A_{i,j} being the number of atoms of type LaTeX: i in one mole of species LaTeX: j. The equation, LaTeX: Ax=b, is mass balance. (Its significance is that it was an early application to show how an LP approach can apply to a nonlinear mathematical program.)

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