Related papers: Stability of a regularized Newton method with two …
This work deals with the problem of stabilizing a multi-agent rigid formation on a general class of planar curves. Namely, we seek to stabilize an equilateral polygonal formation on closed planar differentiable curves after a path sweep.…
Relying on the premise that the performance of a binary neural network can be largely restored with eliminated quantization error between full-precision weight vectors and their corresponding binary vectors, existing works of network…
Stability of nonconvex quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces is investigated. We present several stability properties of the global solution map, and the continuity of the optimal…
This paper considers the problems of solving monotone variational inequalities with H\"older continuous Jacobians. By employing the knowledge of H\"older parameter $\nu$, we propose the $\nu$-regularized extra-Newton method within at most…
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
The rotated multipliers method is performed in the case of the boundary stabilization by means of a(linear or non-linear) Neumann feedback. this method leads to new geometrical cases concerning the "active" part of the boundary where the…
We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our geometric setting is that of a domain whose…
Nonlinearity continuation method, applied to boundary value problems for steady-state Richards equation, gradually approaches the solution through a series of intermediate problems. Originally, the Newton method with simple line search…
Many inverse problems are concerned with the estimation of non-negative parameter functions. In this paper, in order to obtain non-negative stable approximate solutions to ill-posed linear operator equations in a Hilbert space setting, we…
We study stability of a generalized sine-Gordon model with two coupled scalar fields in two dimensions. Topological soliton solutions are found from the first-order equations that solve the equations of motion. The perturbation equations…
This work links optimization approaches from hierarchical least-squares programming to instantaneous prioritized whole-body robot control. Concretely, we formulate the hierarchical Newton's method which solves prioritized non-linear…
The goal of this paper is to investigate the stability of the Helmholtz equation in the high- frequency regime with non-smooth and rapidly oscillating coefficients on bounded domains. Existence and uniqueness of the problem can be proved…
In this paper, we study the phenomenon of increasing stability in the inverse boundary value problems for the biharmonic equation. By considering a linearized form, we obtain an increasing Lipschitz-like stability when k is large.…
In this article, two types of methods from different perspectives based on spectral normalization are described for ensuring the stability of the system controlled by a neural network. The first one is that the L2 gain of the feedback…
This paper is concerned with the study of regularity and stability properties of two Euler-Bernoulli beam equations with localized singular damping. Under suitable regularity assumptions on the damping coefficient, we establish Gevrey…
We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the…
This paper pursues a two-fold goal. Firstly, we aim to derive novel second-order characterizations of important robust stability properties of perturbed Karush-Kuhn-Tucker systems for a broadclass of constrained optimization problems…
This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to…
We study the dynamics of a quantum system having Hilbert space of finite dimension $d_{\mathrm{H}}$. Instabilities are possible provided that the master equation governing the system's dynamics contain nonlinear terms. Here we consider the…
We study numerically stabilized solutions of the two-dimensional Schrodinger equation with a cubic nonlinearity. We discuss in detail the numerical scheme used and explain why choosing the right numerical strategy is very important to avoid…