Related papers: Improving Newton's method performance by parametri…
This paper proposes a novel method for designing finite-horizon discrete-valued switching signals in linear switched systems based on discreteness-promoting regularization. The inherent combinatorial optimization problem is reformulated as…
We propose a stochastic variance-reduced cubic regularized Newton method for non-convex optimization. At the core of our algorithm is a novel semi-stochastic gradient along with a semi-stochastic Hessian, which are specifically designed for…
We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
In this paper, we propose a third-order Newton's method which in each iteration solves a semidefinite program as a subproblem. Our approach is based on moving to the local minimum of the third-order Taylor expansion at each iteration,…
In this paper, we revisit the chaotic number of iterations needed by Newton's method to converge to a root. Here, we consider a simple modified Newton method depending on a parameter. It is demonstrated using polynomiography that even in…
This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors resulting from numerical approximation. To construct our…
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…
This work concerns the local convergence theory of Newton and quasi-Newton methods for convex-composite optimization: minimize f(x):=h(c(x)), where h is an infinite-valued proper convex function and c is C^2-smooth. We focus on the case…
We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…
The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…
In recent publications, the author and his coworkers have proposed a multigrid method for solving linear systems arizing from the discretization of partial differential equations in isogeometric analysis and have proven that the convergence…
Nonlinear systems of partial differential equations (PDEs) may permit several distinct solutions. The typical current approach to finding distinct solutions is to start Newton's method with many different initial guesses, hoping to find…
We study a one dimensional model for two-phase flows in heterogeneous media, in which the capillary pressure functions can be discontinuous with respect to space. We first give a model, leading to a system of degenerated non-linear…
Although persistent excitation is often acknowledged as a sufficient condition to exponentially converge in the field of adaptive parameter estimation, it must be noted that in practical applications this may be unguaranteed. Recently, more…
Numerical analysis is conducted for a generalized particle method for a Poisson equation. Unique solvability is derived for the discretized Poisson equation by introducing a connectivity condition for particle distributions. Moreover, by…
Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method. A…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
Stochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely the Hamilton-Jacobi-Bellman (HJB) equation. In general, this equation cannot be solved analytically, thus numerical algorithms are the…
We propose finite difference methods for degenerate fully nonlinear elliptic equations and prove the convergence of the schemes. Our focus is on the pure equation and a related free boundary problem of transmission type. The cornerstone of…