Efficient hybrid methods for global continuous optimization based on simulated annealing

We introduce several hybrid methods for global continuous optimization. They combine simulated annealing and a local proximal bundle method. Traditionally, the simplest hybrid of a global and a local solver is to call the local solver after the global one, but this does not necessarily produce good results. Besides, using efficient gradient-based local solvers implies that the hybrid can only be applied to differentiable problems. We show several ways how to integrate the local solver as a genuine part of simulated annealing to enable both efficient and reliable solution processes. When using the proximal bundle method as a local solver, it is possible to solve even nondifferentiable problems. The numerical tests show that the hybridization can improve both the efficiency and the reliability of simulated annealing.