English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the problem of finding global minimizers of$V(x):\mathbb{R}^d\rightarrow\mathbb{R}$ approximately via sampling from aprobability distribution $\mu_{\sigma}$ with density$p_{\sigma}(x)=\dfrac{\exp(-V(x)/\sigma)}{\int_{\mathbb R^d} \exp(-V(y)/\sigma)dy }$ with respect to the Lebesgue measure for $\sigma \in (0,1]$ small enough.  We analyze a sampler based on the Euler-Maruyama discretization of theSchr{\"o}dinger-F{\"o}llmer diffusion processes with stochastic approximationunder appropriate assumptions on the step size $s$ and the potential $V$.  We prove that the output of the proposed sampler is an approximate globalminimizer of $V(x)$ with high probability at cost of sampling$\mathcal{O}(d^{3})$ standard normal random variables.  Numerical studies illustrate the effectiveness of the proposed method and itssuperiority to the Langevin method.

Global Optimization via Schr{\"o}dinger-F{\"o}llmer Diffusion