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Speaker: Federica Ferrarese, University of Ferrara, Department of Mathematics and Computer Sciences
Title: Particle-based approaches for enhanced exploration in global optimization
Abstract: The numerical solution of global optimization problems for non-convex and high dimensional functions remains a challenging task, especially in settings where gradient information is unavailable or unreliable. While classical gradient-based methods may suffer from high computational costs and sensitivity to local minima, particle based and stochastic approaches have recently gained significant attention. In this talk, we focus on kinetic-based optimization (KBO) methods, a class of gradient-free algorithms inspired by collective dynamics and mean-field models. These methods rely on interacting agents that explore the optimization landscape through a balance of exploration and concentration mechanisms. We discuss recent developments that incorporate adaptive population dynamics and genetic-type interactions, enhancing robustness and flexibility in complex environments. Particular emphasis is placed on KBO models with fractional diffusion, which introduce non-local stochastic effects and offer improved exploration capabilities in highly non-convex or multi-modal landscapes. We present analytical insights and illustrate their performance through numerical experiments, highlighting their potential advantages over standard diffusion-based approaches.