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Proximal-Based Adaptive Simulated Annealing for Global Optimization

Simulated annealing (SA) is a widely used approach to solve global optimization problems in signal processing. The initial non-convex problem is recast as the exploration of a sequence of Boltzmann probability distributions, which are increasingly harder to sample from. They are parametrized by a temperature that is iteratively decreased, following the so-called cooling schedule. Convergence results of SA methods usually require the cooling schedule to be set a priori with slow decay. In this work, we introduce a new SA approach that selects the cooling schedule on the fly. To do so, each Boltzmann distribution is approximated by a proposal density, which is also sequentially adapted. Starting from a variational formulation of the problem of joint temperature and proposal adaptation, we derive an alternating Bregman proximal algorithm to minimize the resulting cost, obtaining the sequence of Boltzmann distributions and proposals. Numerical experiments in an idealized setting illustrate the potential of our method compared with state-of-the-art SA algorithms.