Given a fixed starting point, we study a finite-horizon optimal control problem, where we want to minimize a weighted sum of an end-point cost and the squared 2-norm of the control. This functional induces a gradient flow on the Hilbert space of admissible controls, and we prove a ...
It is a curve {\varvec{u}} \in AC^{\theta }_{\textrm{loc}}\big ([0,\infty ),{\mathscr {S}}\big ) that satisfies {\varvec{u}}(0)=u_0 and the energy dissipation equality \begin{aligned} \displaystyle \phi ({\varvec{u}}(t))-\phi ({\varvec{u}}(s)) = -\frac{1...
are in accordance with the Guide for the Care and Use of Laboratory Animals61and ARRIVE guidelines56. Fish were transported to the laboratory following the Official Mexican Norm NOM-051-ZOO-1995 for humanitarian treatment in the mobilisation of animals. Laboratory protocols followed all guidelines pro...
The search direction can also be the approximated gradient normalized by its infinity norm. This enables a more appropriate guess for the initial step size (Do and Reynolds, 2013). The framework is presented in Framework 1. Framework 1 This framework has been abundantly used within production ...
An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems 来自 iAacademic 喜欢 0 阅读量: 2300 作者:KC Toh,S Yun 摘要: The affine rank minimization problem, which consists of finding a matrix of minimum rank subject to linear equality constraints, ...
The aim of the norm test is to promote search directions that are close to the true gradient. More recently [8], Bollapragada and coauthors proposed to replace the norm test by another procedure, called augmented inner product test, which ensures that the search direction is a descent ...
The quantities are used to derive closed form expressions for information field analysis using least squares. The expressions are used to estimate $L^2$-Norm of FD and $L^2$-Norm of GFD based contrasts.doi:10.48550/arXiv.1504.02712Dharmani Bhaveshkumar C...
We use L2-Norm to quantify the magnitude. where w is obtained by Equ. (11). Considering ∂ Lold (θt ,Mi ) ∂θt is the summation of the shared gradient g¯ and its task- specific gradient gˆ, the loss change of episodic memory Mi will be negativ...
A weighted norm inequality involving A 1 weights is obtained at the natural exponent for gradients of solutions to quasilinear elliptic equations in Reifenberg flat domains. Certain gradient estimates in Lorentz–Morrey spaces below the natural exponent are also obtained as a consequence of our ...
We call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of...