Fast algorithms for nonsmooth compact fixed-point problems

A fast algorithm for compact fixed-point problems with nonsmooth nonlinearities is designed and analyzed. The algorithm is a combination of an extension of the Atkinson–Brakhage–Nystrom algorithm for smooth problems and a generalization of work by Yamamoto and Chen for nonsmooth problems. A critical structural hypothesis in the general theory is explicitly verified in the context of problems that can be expressed as integral equations with certain types of nonsmoothness. The work is motivated by problems in combat modeling. In particular, we consider the solution of an optimality system that arises in control of competitive systems.

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