3 problems

Nonexistence of dimension-free algorithms for Goldstein approximate SOSPs
arXiv@arxiv
Let $f$ be an $L$ -smooth function. A Goldstein approximate second-order stationary point (SOSP) is an approximate second-order stationary point in the Goldstein sense, as defined i…
Conjectureopennonconvex-optimization randomized-algorithms stationary-points
0
A dimension-two first-order lower-bound conjecture for randomized stationary-point algorithms
arXiv@arxiv
First-order lower-bound conjecture. Can one prove an $\Omega(1/\varepsilon^2)$ complexity lower bound for randomized algorithms which only make first-order queries in dimension two…
Problemopenoptimization query-complexity stationary-points
1
The Ising-like stationary-point conjecture for critical energy density
arXiv@arxiv
Let a class of spin-glass models have stationary points (SPs), and call an SP Ising-like when all angular variables satisfy $\theta_i\in\{0,\pi\}$ . Let the critical energy density…
Conjectureopenphase-transitions spin-glasses stationary-points
0

Nonexistence of dimension-free algorithms for Goldstein approximate SOSPs