Summary: We describe a primal-dual application of the proximal point algorithm to nonconvex minimization problems. Motivated by the work of J. E. Spingarn
[Math. Program. 32, 199–223 (1985; Zbl 0565.90058
)] and more recently by the work of A. Hamdi
et al. [Lect. Notes Econ. Math. Syst. 452, 90–104 (1997; Zbl 0882.65055
)] about the primal resource-directive decomposition scheme to solve nonlinear separable problems. This paper discusses some local results of a primal-dual regularization approach that leads to a decomposition algorithm.