Lagrangian relaxation is useful to bound the optimal value of a given optimization problem, and also to obtain relaxed solutions. To obtain primal solutions, it is conceivable to use a convexification procedure suggested by D.P. Bertsekas in 1979, based on the proximal algorithm in the primal space. The present paper studies the theory assessing the approach in the framework of combinatorial optimization. Our results indicate that very little can be expected in theory, even though fairly good practical results have been obtained for the unit-commitment problem.