2022/07/20 by Yalcin, Gulcin Dinc, Curtis, Frank E.
#49M37 #65K05 #90C26 #90C30 #90C53 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2207.09788
Algorithms for solving nonconvex, nonsmooth, finite-sum optimization problems are proposed and tested. In particular, the algorithms are proposed and tested in the context of an optimization problem formulation arising in semi-supervised machine learning. The common feature of all algorithms is that they employ an incremental quasi-Newton (IQN) strategy, specifically an incremental BFGS (IBFGS) strategy. One applies an IBFGS strategy to the problem directly, whereas the others apply an IBFGS strategy to a difference-of-convex reformulation, smoothed approximation, or (strongly) convex local approximation. Experiments show that all IBFGS approaches fare well in practice, and all outperform a state-of-the-art bundle method.