A unified convergence framework for nonmonotone inexact decomposition methods

In this work we propose a general framework that provides a unified convergence analysis for nonmonotone decomposition algorithms. The main motivation to embed nonmonotone strategies within a decomposition approach lies in the fact that enforcing the reduction of the objective function could be unnecessarily expensive, taking into account that groups of variables are individually updated. We define different search directions and line searches satisfying the conditions required by the presented nonmonotone decomposition framework to obtain global convergence. We employ a set of large-scale network equilibrium problems as a computational example to show the advantages of a nonmonotone algorithm over its monotone counterpart. In conclusion, a new smart implementation for decomposition methods has been derived to solve numerical issues on large-scale partially separable functions.