Related papers: A note on locking materials and gradient polyconve…
Particle gradient descent, which uses particles to represent a probability measure and performs gradient descent on particles in parallel, is widely used to optimize functions of probability measures. This paper considers particle gradient…
We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…
We provide theory for computing the lower semi-continuous convex envelope of functionals of the type f(x) plus an l2 misfit, and discuss applications to various non-convex optimization problems. The latter term is a data fit term whereas f…
The self-concordant-like property of a smooth convex function is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self-concordant-like property, this concept…
We investigate the computation of the gradient of the value function in parametric convex optimization problems. We derive general expression for the gradient of the value function in terms of the cost function, constraints and Lagrange…
The starting assumptions to study the convergence and complexity of gradient-type methods may be the smoothness (also called Lipschitz continuity of gradient) and the strong convexity. In this note, we revisit these two basic properties…
We report extensive numerical simulations of different models of 2D polymer rings with internal elasticity. We monitor the dynamical behavior of the rings as a function of the packing fraction, to address the effects of particle deformation…
Robust discretization methods for (nearly-incompressible) linear elasticity are free of volume-locking and gradient-robust. While volume-locking is a well-known problem that can be dealt with in many different discretization approaches, the…
Local and global weighted norm estimates involving Muckenhoupt weights are obtained for gradient of solutions to linear elliptic Dirichlet boundary value problems in divergence form over a Lipschitz domain $\Omega$. The gradient estimates…
Here we develop a regularity theory for a polyconvex functional in $2\times2-$dimensional compressible finite elasticity. In particular, we consider energy minimizers/stationary points of the functional…
Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study…
This book is devoted to finite-dimensional problems of non-convex non-smooth optimization and numerical methods for their solution. The problem of nonconvexity is studied in the book on two main models of nonconvex dependencies: these are…
Differentiable physics modeling combines physics models with gradient-based learning to provide model explicability and data efficiency. It has been used to learn dynamics, solve inverse problems and facilitate design, and is at its…
The conditions of relative smoothness and relative strong convexity were recently introduced for the analysis of Bregman gradient methods for convex optimization. We introduce a generalized left-preconditioning method for gradient descent,…
We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of…
Convergence of the gradient descent algorithm has been attracting renewed interest due to its utility in deep learning applications. Even as multiple variants of gradient descent were proposed, the assumption that the gradient of the…
The deep energy method (DEM) has been used to solve the elastic deformation of structures with linear elasticity, hyperelasticity, and strain-gradient elasticity material models based on the principle of minimum potential energy. In this…
This study addresses the modelling of elastic bodies, particularly when the relaxed configuration is unknown or non-existent. We adopt the theory of initially stressed materials, incorporating the deformation gradient and stress state of…
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…
The second gradient model of poromechanics, introduced in Part I, is here linearized in the neighborhood of a prestressed reference configuration to be applied to the one-dimensional consolidation problem originally considered by Terzaghi…