A new decomposition method in nonconvex programming via a separable augmented Lagrangian.

*(English)* Zbl 0882.65055
Gritzmann, Peter (ed.) et al., Recent advances in optimization. Proceedings of the 8th French-German conference on Optimization. Trier, Germany, July 21–26, 1996. Berlin: Springer. Lect. Notes Econ. Math. Syst. 452, 90-104 (1997).

Summary: We propose a new decomposition algorithm for separable nonlinear problems with coupling constraints and analyze its local and global convergence properties in the neighbourhood of isolated local minima in the nonconvex case. It can be seen as a separable augmented Lagrangian method based on the primal resource-directive decomposition scheme. Indeed, the primal allocations work as decoupling variables and each local allocation constraint is penalized like in the augmented Lagrangian method. We show how the alternate minimizations of the primal variables and the allocations lead to primal and dual updates which lie in orthogonal subspaces. Some limited numerical results are shown where we analyze the behaviour of the local minima of the subproblems w. r. t. parametric separable allocations.

##### MSC:

65K05 | Mathematical programming (numerical methods) |

90C26 | Nonconvex programming, global optimization |