LOCAL PROXIMAL ALGORITHMS IN RIEMANNIAN MANIFOLDS: APPLICATION TO THE BEHAVIORAL TRAVELER'S PROBLEM

Local proximal point algorithms with quasi distances to find critical points (or minimizer points in the convex case) of functions in finite dimensional Riemannian manifolds are introduced. We prove that bounded sequences of the algorithm generated by proper bounded from below, lower semicontinuous and locally Lipschitz functions have accumulation points which are critical points (minimizer points in the convex case). Moreover, for Kurdyka-Lojasiewicz functions, the sequence globally converges to a critical point. We applied the algorithm to a behavioral traveler’s problem where an individual tries to satisfy locally his needs and desires by moving from one city to the next, with costs to move playing a major role.