Interval methods for solving various kinds of quantified nonlinear problems
Bartłomiej Jacek Kubica
Warsaw University of Technology, Poland
Interval branch-and-bound type methods can be used to sovle various problems, in particular: equations systems, constraint satisfaction problems, global optimization, Pareto sets seeking, Nash points and other game equilibria seeking and other problems, e.g., seeking all local (but non-global) optima of a function.
We show that each of these problems can be expressed by a specific kind of first-order logic formula and investigate, how this affects the structure of the algorithm and used tools. In particular, we discuss several aspects of parallelization of these algorithms.
The focus is on seeking game equilibria, that is a relatively novel application of interval methods.