Related papers: Approximation Properties of a Gradient Recovery Op…
This paper is concerned with the nonconforming finite element discretization of geometric partial differential equations. In specific, we construct a surface Crouzeix-Raviart element on the linear approximated surface, analogous to a flat…
We propose and analyze a randomized zeroth-order approach based on approximating the exact gradient byfinite differences computed in a set of orthogonal random directions that changes with each iteration. A number ofpreviously proposed…
Discrete conjugate systems are quadrilateral nets with all planar faces. Discrete orthogonal systems are defined by the additional property of all faces being concircular. Their geometric properties allow one to consider them as proper…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
We introduce the concept of inexact first-order oracle of degree q for a possibly nonconvex and nonsmooth function, which naturally appears in the context of approximate gradient, weak level of smoothness and other situations. Our…
This paper investigates gradient recovery schemes for data defined on discretized manifolds. The proposed method, parametric polynomial preserving recovery (PPPR), does not require the tangent spaces of the exact manifolds, and they have…
Quaternion-valued signal processing has received increasing attention recently. One key operation involved in derivation of all kinds of adaptive algorithms is the gradient operator. Although there have been some derivations of this…
Several algebraic and topological properties of subgradient projection operators are investigated and various examples are provided. Connections with Moreau's proximity operator are also made and acceleration schemes for subgradient…
This paper reviews gradient-based techniques to solve bilevel optimization problems. Bilevel optimization is a general way to frame the learning of systems that are implicitly defined through a quantity that they minimize. This…
In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…
Projected gradient methods are widely used for constrained optimization. A key application is for partial differential equations (PDEs), where the objective functional represents physical energy and the linear constraints enforce…
Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
Rotation estimation of known rigid objects is important for robotic applications such as dexterous manipulation. Most existing methods for rotation estimation use intermediate representations such as templates, global or local feature…
A new construction of biorthogonal splines for isogeometric mortar methods is proposed. The biorthogonal basis has a local support and, at the same time, optimal approximation properties, which yield optimal results with mortar methods. We…
Superconvergence of differential structure on discretized surfaces is studied in this paper. The newly introduced geometric supercloseness provides us with a fundamental tool to prove the superconvergence of gradient recovery on deviated…
Gradient boosting is a state-of-the-art prediction technique that sequentially produces a model in the form of linear combinations of simple predictors---typically decision trees---by solving an infinite-dimensional convex optimization…
We describe the representation of arbitrary density operators in terms of expectation values of simple projection operators. Two representations are presented which yield non--recursive schemes for experimentally determining the density…
A set of orthonormal polynomials is proposed for image reconstruction from projection data. The relationship between the projection moments and image moments is discussed in detail, and some interesting properties are demonstrated.…