Condensation Effects in a Novel Consensus-Based Optimization Algorithm
Please login to view abstract download link
Consensus-based optimization (CBO) is a class of metaheuristic algorithms that is particularly useful in the context of minimization problems for non-convex, high-dimensional functionals. One of the advantages of CBO is that it can be effectively studied by leveraging its connections to partial differential equations usually arising in the context of mathematical physics, and in particular equations of Fokker-Planck type. In this talk, we introduce a novel consensus-based algorithm that we can formally study from an analytical point of view. We show that its mean-field formulation exhibits condensation effects, with the loss of L2-regularity of the solution and formation of a blow-up in finite time. We also present several numerical tests that demonstrate the consistency of our approach as well as the performance advantages over classical CBO methods.