Related papers: Dimensionally Consistent Preconditioning for Saddl…
We introduce an adaptive element-based domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any knowledge of the constrained space. We assume that all sub…
Critical point tracking is a core topic in scientific visualization for understanding the dynamic behavior of time-varying vector field data. The topological notion of robustness has been introduced recently to quantify the structural…
High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a conservation law solution and align elements of the…
We will present a new general framework for robust and adaptive control that allows for distributed and scalable learning and control of large systems of interconnected linear subsystems. The control method is demonstrated for a linear…
We summarize recent progress on one- and multi-dimensional stability of viscous shock wave solutions of compressible Navier--Stokes equations and related symmetrizable hyperbolic--parabolic systems, with an emphasis on the large-amplitude…
We consider iterative methods for solving the linearised Navier-Stokes equations arising from two-phase flow problems and the efficient preconditioning of such systems when using mixed finite element methods. Our target application is…
In this paper, we consider using Schur complements to design preconditioners for twofold and block tridiagonal saddle point problems. One type of the preconditioners are based on the nested (or recursive) Schur complement, the other is…
The Primal-Dual (PD) algorithm is widely used in convex optimization to determine saddle points. While the stability of the PD algorithm can be easily guaranteed, strict contraction is nontrivial to establish in most cases. This work…
We present a scalable combinatorial algorithm for globally optimizing over the space of geometrically consistent mappings between 3D shapes. We use the mathematically elegant formalism proposed by Windheuser et al. (ICCV 2011) where 3D…
Scaling deep reinforcement learning networks is challenging and often results in degraded performance, yet the root causes of this failure mode remain poorly understood. Several recent works have proposed mechanisms to address this, but…
We consider the problem of iteratively solving large and sparse double saddle-point systems arising from the stationary Stokes-Darcy equations in two dimensions, discretized by the Marker-and-Cell (MAC) finite difference method. We analyze…
Continuous time primal-dual gradient dynamics that find a saddle point of a Lagrangian of an optimization problem have been widely used in systems and control. While the global asymptotic stability of such dynamics has been well-studied, it…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…
On the basis of an analysis of previous research, we present a generalized approach for measuring the difference of plans with an exemplary application to machine scheduling. Our work is motivated by the need for such measures, which are…
In many applications, one wants to model physical systems consisting of two different physical processes in two different domains that are coupled across a common interface. A crucial challenge is then that the solutions of the two…
We study trade-offs between the population risk curvature, geometry of the noise, and preconditioning on the generalisation ability of the multipass Preconditioned Stochastic Gradient Descent (PSGD). Many practical optimisation heuristics…
Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several…
Motivated by the theory of self-duality which provides a variational formulation and resolution for non self-adjoint partial differential equations \cite{G1, G2}, we propose new templates for solving large non-symmetric linear systems. The…
We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…
We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new…