Almost-sure global convergence of the subgradient method for \ell_1-norm rank-one symmetric matrix factorization

Consider the $\ell_1$-norm rank-one symmetric matrix factorization problem and initialize the subgradient method randomly, with an initialization distribution absolutely continuous with respect to Lebesgue measure. Let the step sizes be sufficiently small and diminishing: positive, nonsummable, and converging to zero. Almost-sure global convergence conjecture. The subgradient method converges to a globally optimal solution almost surely. The conjecture is motivated by the observed behavior of subgradient flow away from a lower-dimensional set of spurious stationary points; the supplied text does not state whether the conjecture has been proved or disproved.