Multiplier methods for convex programming

A combined primal-dual and penalty method is given for solving the nonlinear programming problem. The algorithm generalizes the "method of multipliers" and is applicable to problems with both equality and inequality constraints. The algorithm is defined for a broad class of "penalized Lagrangians," and is shown to be globally convergent when applied to the convex programming problem. The duality aspects are explored, leading to geometrical interpretations of the method and its relationship to generalized Lagrange multipliers. The rate of convergence is given and the method is shown to be superior to ordinary penalty methods.