On primal convergence for augmented Lagrangian duality
Regina Sandra Burachik · Optimization · 2011
We study some theoretical properties of augmented Lagrangian duality schemes for nonconvex and nonsmooth optimization. These schemes may not have primal convergence, in the sense that limit points of the primal sequence may not solve the primal problem. First, we prove that primal convergence holds if and only if the dual function is differentiable at the dual limit. Second, we relate the latter differentiability property with the existence of exact penalty parameters. Finally, we give a condition on the Lagrangian which ensures that every point supports an exact penalty representation.