Adaptive Descent Splitting Method for Decomposable Optimization Problems

Abstract

© 2020, Springer Nature Switzerland AG. We suggest a modified descent splitting method for optimization problems having a special decomposable structure. The proposed modification maintains the basic convergence properties but enables one to reduce computational efforts per iteration and to provide computations in a distributed manner. On the one hand, it consists in component-wise choice of descent directions together with a special threshold control. On the other hand, it involves a simple adaptive step-size choice, which takes into account the problem behavior along the iteration sequence. Preliminary computational tests confirm the efficiency of the proposed modification.