11 problems

Midpoint constraint-violation conjecture. The constraint violation bound under the midpoint method scales as

Let $\Pi\texttt{net}$ denote the method studied in this paper, let $\texttt{DC3}$ denote the comparison method, and let $\texttt{RS}$ denote the reported residual metric. The train…

Approximate multiplier convergence conjecture. Under the direct-adjoining and secant-function-augmentation formulations, $\tilde{\eta}_i$ approaches $\eta_i$ as $\rho_i\to 0$:

Consider the positivity-constrained Gaussian inverse problem … where $\bK\in\mathbb{R}^{m\times p}$ is a forward linear operator, not necessarily of full column rank, and let…

A decision set is a bounded polyhedron, also called a polytope, or a convex set, and a warping is a transformation used to formulate optimization over the interior of a constrained…

Consider the affine-constrained case in which ${\mathbf{c}}({\mathbf{x}})={\mathbf{A}}{\mathbf{x}}-{\mathbf{b}}$, and let $h$ denote the nonsmooth term in the composite objective.…

Physics-constrained (informed) learning concerns using neural networks to learn solutions of partial differential equations while incorporating physical constraints. The non-convex…

Consider the perturbed constrained optimization problem … where … Assume that at $t=0$ there is a unique optimal solution $z_0$ with a unique Lagrangian multiplier $v_0$, let…

Let $A$ be the set of arms, let $A_f$ be the set of feasible arms, and let $\Pi$ denote the set of deterministic algorithms for the constrained multi-armed bandit problem. An algor…

Constraint-specific explanation conjecture. The difference between the results obtained for the paper's RMAB constraints and those obtained for the more general WCDP constraints is…

Frictional convergence conjecture. Even a small amount of friction prohibits convergence to non-Nash profiles.