11 problems

Subgradient dominance conjecture. $s$-rectangular RMDPs satisfy the subgradient dominance property, and subgradient dominance can hold under conditions weaker than uniqueness of th…

Let $f$ be a semialgebraic function with a stratification of its graph, let $\cX$ denote the relevant stratum, and let $\partial\cX$ and $\sX_{\dim(\cX)-1}$ denote its boundary and…

Specular-gradient conjecture. The function $f$ is convex on $U$ if and only if

Consider the $\ell_1$-norm rank-one symmetric matrix factorization problem and initialize the subgradient method randomly, with an initialization distribution absolutely continuous…

The stochastic conjugate subgradient (SCS) algorithm is an online method for stochastic convex optimization, while stochastic gradient descent (SGD) methods are stochastic first-or…

For second-order variational penalties, let $\ia_i(\ix_{i-1},\ix_i)$ be the piecewise linear manifold in $\reals^2$ whose facets are stored as triplets $\{v_j^1,v_j^2,\alpha_j\}$.…

Consider the subgradient method for minimizing a function with initial-distance parameter $R$ and subgradient-bound parameter $B$, and suppose that its step sizes are chosen indepe…

Let $f$ be a locally Lipschitz definable function, and let a continuous subgradient trajectory of $f$ have orbit $\mathcal{O}$. A trajectory is nonoscillatory if its intersection w…

Sub-gradient identification conjecture. The true solutions identified by the sub-gradient method applied to the $\ell_1$-loss might be non-active strict saddle points.

Subgradient-norm convergence conjecture. For every iterate $x_N$, there exists a subgradient $g_N\in\partial f(x_N)$ such that

Generic convergence conjecture. For a full-measure set of vectors $v\in\mathbf{R}^n$, the subgradient method applied to $f_v$ either diverges or converges to a local minimizer of…