  The Sherrington-Kirkpatrick (SK) model is a prototype of a complex non-convex
energy landscape. Dynamical processes evolving on such landscapes and locally
aiming to reach minima are generally poorly understood. Here, we study
quenches, i.e. dynamics that locally aim to decrease energy. We analyse the
energy at convergence for two distinct algorithmic classes, single-spin flip
and synchronous dynamics, focusing on greedy and reluctant strategies. We
provide precise numerical analysis of the finite size effects and conclude
that, perhaps counter-intuitively, the reluctant algorithm is compatible with
converging to the ground state energy density, while the greedy strategy is
not. Inspired by the single-spin reluctant and greedy algorithms, we
investigate two synchronous time algorithms, the sync-greedy and sync-reluctant
algorithms. These synchronous processes can be analysed using dynamical mean
field theory (DMFT), and a new backtracking version of DMFT. Notably, this is
the first time the backtracking DMFT is applied to study dynamical convergence
properties in fully connected disordered models. The analysis suggests that the
sync-greedy algorithm can also achieve energies compatible with the ground
state, and that it undergoes a dynamical phase transition.
