Related papers: Inexact Newton Method for General Purpose Reservoi…
An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…
This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a…
We study a variant of Newton's algorithm applied to under-determined systems of non-smooth equations. The notion of regularity employed in our work is based on Newton differentiability, which generalizes semi-smoothness. The classic notion…
A class of interior point methods using inexact directions is analysed. The linear system arising in interior point methods for linear programming is reformulated such that the solution is less sensitive to perturbations in the right-hand…
Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses local Quasi-Newton…
The objective of this publication is to reduce the sensitivity of iterative equation solvers on the initial value. To this end, at the hand of Newton's method, we exemplify how to reformulate the initial problem by means of a set of…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
As an effective emulator of ill-conditioned power flow, continuous Newton methods (CNMs) have been extensively investigated using explicit and implicit numerical integration algorithms. Explicit CNMs are prone to non-convergence issues due…
Computing the regularized solution of Bayesian linear inverse problems as well as the corresponding regularization parameter is highly desirable in many applications. This paper proposes a novel iterative method, termed the Projected Newton…
We analyze inexact fixed point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed point…
We study stochastic inexact Newton methods and consider their application in nonconvex settings. Building on the work of [R. Bollapragada, R. H. Byrd, and J. Nocedal, IMA Journal of Numerical Analysis, 39 (2018), pp. 545--578] we derive…
Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly solved by the fully-implicit scheme.…
For nonlinear equations, the homotopy methods (continuation methods) are popular in engineering fields since their convergence regions are large and they are quite reliable to find a solution. The disadvantage of the classical homotopy…
In this paper, an idea to solve nonlinear equations is presented. During the solution of any problem with Newton's Method, it might happen that some of the unknowns satisfy the convergence criteria where the others fail. The convergence…
We consider the inexact Newton methods $$ x_{n+1}^\d=x_n^\d-g_{\a_n}(F'(x_n^\d)^* F'(x_n^\d)) F'(x_n^\d)^* (F(x_n^\d)-y^\d) $$ for solving nonlinear ill-posed inverse problems $F(x)=y$ using the only available noise data $y^\d$ satisfying…
In this paper we derive a Newton type method to solve the non-linear system formed by combining the Tikhonov normal equations and Morozov's discrepancy principle. We prove that by placing a bound on the step size of the Newton iterations…
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…
We consider a class of inexact Newton regularization methods for solving nonlinear inverse problems in Hilbert scales. Under certain conditions we obtain the order optimal convergence rate result.
In a recent paper an Inexact Restoration method for solving continuous constrained optimization problems was analyzed from the point of view of worst-case functional complexity and convergence. On the other hand, the Inexact Restoration…
This paper presents a novel implicit scheme for the constraint resolution in real-time finite element simulations in the presence of contact and friction. Instead of using the standard motion correction scheme, we propose an iterative…