# Convex simplex method

This extends the general strategy of the simplex method in linear programming to maximize a concave objective over linear constraints of the form $LaTeX: Ax=b$ and $LaTeX: x \ge 0$. (A form of local convergence applies when the objective is not concave, but is smooth.) A tableau is maintained, but nonbasic variables need not be at zero level. The partition is used to compute a generalized reduced cost of the form $LaTeX: d(x) = \nabla f(x) - y^T A$. The $LaTeX: y$ vector is determined by the basic portion: $LaTeX: 0 = \nabla_B f(x) - y^TB$ (so $LaTeX: y = (\nabla_B f(x))B^{-1}$).