אופטימיזציה גלובלית מהירה

תקציר מקורי באנגליתarXiv:2609.06196v1 Announce Type: cross Abstract: We study the computational effort required for global optimization of a smooth, possibly nonconvex objective $\Gamma:\mathbb{R}^d\to\mathbb{R}$. An algorithm satisfies the $(\varepsilon,\delta)$-PAC performance requirement if its output $\widehat X$ obeys $\mathbb{P}\{\Gamma(\widehat X)-\Gamma^\star>\varepsilon\}\leq\delta$. Algorithm design and analysis are in continuous time. We compare classical simulated annealing and fixed-temperature Langevin diffusion with two approaches introduced and analyzed here: parallel-restart Langevin and a Langevin--gradient scheme using stochastic dynamics for global exploration and gradient flow for local exploitation. Let $L=\log(1/\delta)$ and let $E_*$ denote the dominant energy barrier. At logarithmic