20 problems

In the fictitious-play setting, let $A\in\mathbb{R}^{n\times n}$ be the identity matrix, and consider the convergence rate measured by the relevant gap function. Karlin's conjectur…

Let $V^+$ and $V^-$ be the upper and lower value functions of the stochastic differential game of mixed type, defined by … and … Here $\mathcal{A}_1$ and $\mathcal{A}_2$ are the ad…

Let Problem 3.1 be the quasi-variational–hemivariational inequality whose unknown is a flow velocity…

The adaptive delayed-update cyclic algorithm is defined with step sizes and extrapolation weights as above, where $bc$ denotes the strong convexity parameter used in the theoretica…

Path-graph conjecture. For every integer $n\geqslant3$,

Liu–Xue's conjecture. The optimal constant for the star graph is the same as for the complete graph, namely

Liu–Xue's conjecture. For every integer $n\geqslant3$ and every $p\in(0,\infty)$,

The latent variable proximal point (LVPP) algorithm generates a sequence of proximal parameters $(\alpha_k)_{k\in\mathbb{N}}$, and for the obstacle problem convergence to its solut…

Let the bedrock elevation and surface mass balance be fixed over a land region, and consider the continuous-space, implicit time-step free-boundary problem for the glacier surface…

Consider constrained, $L$-smooth min-max problems that may be stochastic and nonconvex-nonconcave, satisfying $\rho$-cohypomonotonicity or admitting a solution to the $\rho$-weakly…

Consider the proximal Galerkin method for pointwise bound-constrained problems, and suppose that the problem satisfies a strict complementarity condition. Strict-complementarity co…

The paper studies regularized variational inequality problems and develops a unified analysis for stochastic gradient descent-ascent-type methods fitting a specified general scheme…

Let $\mathcal{M}^*$ denote the nonempty solution set of $\operatorname{VI}(\theta,\mathcal{J},\mathcal{M})$, where … The proposed P-ALM generates a sequence characterized by an ine…

Consider optimistic gradient (OG) applied to the setting discussed in the paper, with step size $\eta$ and a vector field satisfying the relevant smoothness and strong monotonicity…

Let $T$ be a Calderón–Zygmund operator with a standard kernel, and let $\{\varepsilon_j\}_j$ be a fixed sequence with $\varepsilon_j\to0$ such that, for every…

Let $\current[\stepalt]$ and $\current[\step]$ denote the two stepsizes in the generalized optimistic gradient recursion, and let $\current$ and $\last[\svecfield]$ denote the curr…

Consider monotone inclusion problems with an operator whose relevant properties include Lipschitz continuity, cocoercivity, or strong monotonicity, and let $L$, $m$, $D$, and…

Cox–Wang extension conjecture. By slightly changing the terminal condition in the variational inequality, the variational-inequality construction of Root's embeddings should extend…

Zero-boundary derivative conjecture. The boundary condition

Let $F$, $x^\dagger$, $Y$, and $\mathcal{M}_{\alpha_{\max}}(\rho)$ be as in the nonlinear inverse problem under consideration. An index function $\sigma$ is a function appearing in…