Stochastic Continuation - Opening New Horizons to Solving Difficult Optimization Problems

Simulated annealing (SA) and its deterministic analog, namely continuation, are well-known approaches to global optimization. SA is asymptotically optimal but converges very slowly, whereas deterministic continuation is much less computationally demanding but is suboptimal. In this paper, we introduce a new class of hybrid algorithms which combines the theoretical advantages of SA with the practical advantages of deterministic continuation. We call this class of algorithms stochastic continuation (SC). We show that SC inherits the convergence properties of generalized SA under fairly mild assumptions and that it can be successfully applied to piecewise constant signal reconstruction. Our numerical experiments indicate that SC substantially outperforms SA.