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Algorithms for solving nonconvex, nonsmooth, finite-sum optimization problemsare proposed and tested. In particular, the algorithms are proposed and testedin the context of an optimization problem formulation arising insemi-supervised machine learning. The common feature of all algorithms is thatthey employ an incremental quasi-Newton (IQN) strategy, specifically anincremental BFGS (IBFGS) strategy. One applies an IBFGS strategy to the problemdirectly, whereas the others apply an IBFGS strategy to a difference-of-convexreformulation, smoothed approximation, or (strongly) convex localapproximation. Experiments show that all IBFGS approaches fare well inpractice, and all outperform a state-of-the-art bundle method.

Incremental Quasi-Newton Algorithms for Solving Nonconvex, Nonsmooth, Finite-Sum Optimization Problems