10 problems

The mean-field Potts model has state space $\Omega=[q]^n$, and the annealed single-site Glauber dynamics is initialized from $\mu_{\beta_0}$ for a constant…

Let $(\rho_t)_{t\geq 0}$ be the curve of marginal laws associated with the controlled swarm gradient dynamics, and let $\rho_\infty$ denote its limiting measure. Let $\beta(t)$ be…

Consider the modified Rastrigin function … Numerical simulations exhibit local minima whose values are close to the global minimum, with samples potentially remaining at a local mi…

Let the techniques developed in this paper be applied to optimization problems with objectives having multiple local minima, and let simulated annealing be used as a comparison met…

Consider a finite sample for which the critical temperatures $T_\text{\tiny KS}$ and $T_d$ are estimated by belief-propagation stability analyses. For each paired sample estimate,…

Simulated-annealing threshold conjecture. The quantity $c_\text{\tiny SA}$ is the algorithmic threshold for simulated annealing: for $c>c_\text{\tiny SA}$, simulated annealing achi…

Let an atomic-strata sampling design use a simulated annealing method that selects atomic strata for exchange. Atomic strata near stratum boundaries are distinguished from more imp…

Adaptive exploration conjecture. Although the preceding theoretical guarantees may not hold with the same bounds because the time dependence in the upper bound is through…

SQA efficiency conjecture. SQA will be efficient for all parameter values satisfying

Extension conjecture. The second part of the corollary holds for any $\nu\geq 1$; namely, if $\lim_{n\rightarrow\infty}\sigma_{n,i}=0$ for all $i$, then conditions $-$ hold under