Related papers: On improving the numerical convergence of highly n…
We investigate new convex relaxations for the pooling problem, a classic nonconvex production planning problem in which input materials are mixed in intermediate pools, with the outputs of these pools further mixed to make output products…
A molecular-dynamics type simulation method, which is suitable for investigating the dewetting dynamics of thin and viscous liquid layers, is discussed. The efficiency of the method is exemplified by studying a two-parameter depinning-like…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
We present a Newton-Krylov solver for a viscous-plastic sea-ice model. This constitutive relation is commonly used in climate models to describe the material properties of sea ice. Due to the strong nonlinearity introduced by the material…
This work comprises a detailed theoretical and computational study of the boundary value problem for transversely isotropic linear elastic bodies. General conditions for well-posedness are derived in terms of the material parameters. The…
This paper represents a sequel to the previous one, where numerical solution of a quasistatic contact problem is considered for an elastic body in frictional contact with a moving foundation. The model takes into account wear of the contact…
The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give estimates…
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…
We analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of the shell becomes small. We prove robust convergence of the…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…
We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer…
This work investigates the morphological stability of a soft body composed of two heavy elastic layers, attached to a rigid surface and subjected only to the bulk gravity force. Using theoretical and computational tools, we characterize the…
We learn parameterized nonlinear elasticity on curved surfaces using a physics-informed neural network that enforces governing equations and boundary conditions directly through the loss function, enabling a single trained model to…
Many problems of theoretical and practical interest involve finding a convex or concave function. For instance, optimization problems such as finding the projection on the convex functions in $H^k(\Omega)$, or some problems in economics. In…
The first part of the cumulative thesis contains the numerical analysis of different $hp$-finite element discretizations related to two different weak formulations of a model problem in elastoplasticity with linearly kinematic hardening.…
The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient Scheme framework can be adapted to elasticity equations, and…
Newton-type methods enjoy fast local convergence and strong empirical performance, but achieving global guarantees comparable to first-order methods remains challenging. Even for simple strongly convex problems, no straightforward variant…