A Primal–Dual Penalty Method via Rounded Weighted-\boldmath{$\ell_1$} Lagrangian Duality
We propose a new duality scheme based on a sequence of smooth minorants of the weighted-$\ell_1$ penalty function, interpreted as a parametrized sequence of augmented Lagrangians, to solve nonconvex and nonsmooth constrained optimization problems. For the induced sequence of dual problems, we establish strong asymptotic duality properties. Namely, we show that (i) the sequence of … Read more