Parallel Uzawa Method for Large‐Scale Minimization of Partially Separable Functions

A parallel Uzawa‐type algorithm, for solving unconstrained minimization of large‐scale partially separable functions, is presented. Using auxiliary unknowns, the unconstrained minimization problem is transformed into a (linearly) constrained minimization of a separable function.The augmented Lagrangian of this problem decomposes into a sum of partially separable augmented Lagrangian functions. To take advantage of this property, a Uzawa block relaxation is applied. In every iteration, unconstrained minimization subproblems are solved in parallel before updating Lagrange multipliers. Numerical experiments show that the speed‐up factor gained using our algorithm is significant.