Draft:Consensus based optimization

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Consensus-based optimization (CBO)^[1] is a multi-agent derivative-free optimization method, designed to obtain solutions for global optimization problems of the form $${\displaystyle \min _{x\in {\cal {X}}}f(x),}$$

where ${\displaystyle f:{\mathcal {X}}\to \mathbb {R} }$ denotes the objective function acting on the state space ${\displaystyle {\cal {X}}}$, which is assumed to be a normed vector space. The function ${\displaystyle f}$ can potentially be nonconvex and nonsmooth. The algorithm employs particles or agents to explore the state space, which communicate with each other to update their positions. Their dynamics follows the paradigm of metaheuristics, which blend exporation with exploitation. In this sense, CBO is comparable to ant colony optimization, wind driven optimization^[2], particle swarm optimization or Simulated annealing.