Minima distribution for global optimization
This provides a foundational theoretical framework for global optimization, potentially impacting all of ML/AI, though it appears incremental in extending known conditions.
The paper establishes a strict mathematical relationship between an arbitrary continuous function on a compact set and its global minima, constructing sequences that monotonically converge to the global minima and shrink sets to the minimizers with determinable rates for differentiable functions.
This paper establishes a strict mathematical relationship between an arbitrary continuous function on a compact set and its global minima, like the well-known first order optimality condition for convex and differentiable functions. By introducing a class of nascent minima distribution functions that is only related to the target function and the given compact set, we construct a sequence that monotonically converges to the global minima on that given compact set. Then, we further consider some various sequences of sets where each sequence monotonically shrinks from the original compact set to the set of all global minimizers, and the shrink rate can be determined for continuously differentiable functions. Finally, we provide a different way of constructing the nascent minima distribution functions.