Related papers: Newton's method for nonlinear mappings into vector…
The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the method has not been proven to be able to handle extreme…
This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable…
We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone…
In this paper, we consider the inverse eigenvalue problem for the positive doubly stochastic matrices, which aims to construct a positive doubly stochastic matrix from the prescribed realizable spectral data. By using the real Schur…
The nonlinear eigen-problem $ Ax+F(x)=\lambda x$ is studied where $A$ is an $n\times n$ irreducible Stieltjes matrix. Under certain conditions, this problem has a unique positive solution. We show that, starting from a multiple of the…
We extend the class of SQP methods for equality constrained optimization to the setting of differentiable manifolds. The use of retractions and stratifications allows us to pull back the involved mappings to linear spaces. We study local…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…
Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such…
In this work we present and discuss a possible globalization concept for Newton-type methods. We consider nonlinear problems $f(x)=0$ in $\mathbb{R}^{n}$ using the concepts from ordinary differential equations as a basis for the proposed…
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate…
A general formulation of zero curvature connections in a principle bundle is presented and some applications are discussed. It is proved that a related connection based on a prolongation in an associated bundle remains zero curvature as…
We introduce vector bundle techniques for finding equations of secant varieties. A test is established that determines when a secant variety is an irreducible component of the zero set of the equations found. We also prove an induction…
We consider the inverse problem of recovering a connection on a complex vector bundle over a compact smooth Riemannian manifold with boundary from a Dirichlet-to-Neumann (DN) map at a high fixed frequency. We construct Gaussian beams using…
Let $E$ be a uniformly smooth and uniformly convex real Banach space and $E^*$ be its dual space. Suppose $A : E\rightarrow E^*$ is bounded, strongly monotone and satisfies the range condition such that $A^{-1}(0)\neq \emptyset$. Inspired…
In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…
In this paper we generalize the technique of deflation to define two new methods to systematically find many local minima of a nonlinear least squares problem. The methods are based on the Gauss-Newton algorithm, and as such do not require…
The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We…
We present an iterative root finding method for harmonic mappings in the complex plane, which is a generalization of Newton's method for analytic functions. The complex formulation of the method allows an analysis in a complex variables…
We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal…
Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions,…