Primal-Dual Lagrangian Transformation method for Convex Optimization

Received: date / Revised version: date Abstract. A class Ψ of strongly concave and smooth functions ψ : R → R with specific properties is used to transform the terms of the classical Lagrangian associated with the constraints. The transformation is scaled by a positive vector of scaling parameters, one for each constraint. Each step of the Lagrangian Transformation (LT) method alternates unconstrained minimization of LT in primal space with both Lagrange multipliers and scaling parameters update. Our main focus is on the primal-dual LT method. We introduce the primal-dual LT method and show that under the standard second order optimality condition the method generates a primal-dual sequence that globally converges to the primal-dual solution with asymptotic quadratic rate.