Related papers: Sobolev Gradients for the M\"obius Energy
We are concerned with conservative systems $\ddot{q}=\nabla V(q), \; q\in\mathbb{R}^N$ for a general class of potentials $V\in C^1(\mathbb{R}^N)$. Assuming that a given sublevel set $\{V\leq c\}$ splits in the disjoint union of two closed…
A gradient-based method for shape optimization problems constrained by the acoustic wave equation is presented. The method makes use of high-order accurate finite differences with summation-by-parts properties on multiblock curvilinear…
This paper is concerned with the theory, construction and application of variable-stepsize implicit Peer two-step methods that are super-convergent for variable stepsizes, i.e., preserve their classical order achieved for uniform stepsizes…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
Energy-based fragmentation methods approximate the potential energy of a molecular system as a sum of contribution terms built from the energies of particular subsystems. Some such methods reduce to truncations of the many-body expansion…
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…
Because of the large energy separation between O-K and Mo-L$_{2,3}$ edges, extracting precise and reliable chemical information from core-loss EELS analyze of molybdenum oxides has always been a challenge. In this regard Mo-M$_{2,3}$ edges…
We derive a variational model to fit a composite B\'ezier curve to a set of data points on a Riemannian manifold. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the…
We propose efficient methods for solving stochastic simple bilevel optimization problems with convex inner levels, where the goal is to minimize an outer stochastic objective function subject to the solution set of an inner stochastic…
The equilibrium equations for wide, developable, Moebius strips undergoing large deformations have recently been derived, and solved, numerically. We use these results to compute the eigenvalues and eigenstates of non-interacting electrons…
Gradient-based minimax optimal algorithms have greatly promoted the development of continuous optimization and machine learning. One seminal work due to Yurii Nesterov [Nes83a] established $\tilde{\mathcal{O}}(\sqrt{L/\mu})$ gradient…
While over the last century or more considerable effort has been put into the problem of finding approximate solutions for wave equations in general, and quantum mechanical problems in particular, it appears that as yet relatively little…
We introduce and implement a method to compute stationary states of nonlinear Schr\''odinger equations on metric graphs. Stationary states are obtained as local minimizers of the nonlinear Schr\''odinger energy at fixed mass. Our method is…
The worst case integration error in reproducing kernel Hilbert spaces of standard Monte Carlo methods with n random points decays as $n^{-1/2}$. However, re-weighting of random points can sometimes be used to improve the convergence order.…
The shape gradient quantifies the change in some figure of merit resulting from differential perturbations to a shape. Shape gradients can be applied to gradient-based optimization, sensitivity analysis, and tolerance calculation. An…
Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…
Multi-objective optimization models that encode ordered sequential constraints provide a solution to model various challenging problems including encoding preferences, modeling a curriculum, and enforcing measures of safety. A recently…
The shape gradient is a local sensitivity function that provides the change in a figure of merit associated with a perturbation to the shape of the object. The shape gradient can be used for gradient-based optimization, sensitivity…
This paper contributes to the exploration of a recently introduced computational paradigm known as second-order flows, which are characterized by novel dissipative hyperbolic partial differential equations extending accelerated gradient…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…