Related papers: On a non-archimedean broyden method
Generated Jacobian Equations have been introduced by Trudinger [Disc. cont. dyn. sys (2014), pp. 1663-1681] as a generalization of Monge-Amp{\`e}re equations arising in optimal transport. In this paper, we introduce and study a damped…
We develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear…
We develop and analyze a broad family of stochastic/randomized algorithms for inverting a matrix. We also develop specialized variants maintaining symmetry or positive definiteness of the iterates. All methods in the family converge…
Bayesian methods are often optimal, yet increasing pressure for fast computations, especially with streaming data, brings renewed interest in faster, possibly sub-optimal, solutions. The extent to which these algorithms approximate Bayesian…
The Neumann--Neumann method is a commonly employed domain decomposition method for linear elliptic equations. However, the method exhibits slow convergence when applied to semilinear equations and does not seem to converge at all for…
In recent years, interface quasi-Newton methods have gained growing attention in the fluid-structure interaction community by significantly improving partitioned solution schemes: They not only help to control the inherent added-mass…
In this paper, we study the application of quasi-Newton methods for solving empirical risk minimization (ERM) problems defined over a large dataset. Traditional deterministic and stochastic quasi-Newton methods can be executed to solve such…
Based on differences of points and differences of gradients over the most recent three iterations, together with the Taylor's theorem, two forms of the quasi-Newton equations at the recent iteration are constructed. By using the two forms…
The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of…
We discuss the close connection between eigenvalue computation and optimization using the Newton method and subspace methods. From the connection we derive a new class of Newton updates. The new update formulation is similar to the…
Non-asymptotic analysis of quasi-Newton methods have gained traction recently. In particular, several works have established a non-asymptotic superlinear rate of $\mathcal{O}((1/\sqrt{t})^t)$ for the (classic) BFGS method by exploiting the…
This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical…
In this paper we present GSSN, a globalized SCD semismooth* Newton method for solving nonsmooth nonconvex optimization problems. The global convergence properties of the method are ensured by the proximal gradient method, whereas locally…
In this paper, we propose a quasi Newton method to solve the robust counterpart of an uncertain multiobjective optimization problem under an arbitrary finite uncertainty set. Here the robust counterpart of an uncertain multiobjective…
In this paper, we investigate global convergence properties of the inexact nonsmooth Newton method for solving the system of absolute value equations (AVE). Global $Q$-linear convergence is established under suitable assumptions. Moreover,…
At the heart of Newton based optimization methods is a sequence of symmetric linear systems. Each consecutive system in this sequence is similar to the next, so solving them separately is a waste of computational effort. Here we describe…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization problems or the Jacobian in system of nonlinear equations. In the Interior Point context,…
We present some advances, both from a theoretical and from a computational point of view, on a quadratic vector equation (QVE) arising in Markovian Binary Trees. Concerning the theoretical advances, some irreducibility assumptions are…
We consider a parametric quasi-variational inequality (QVI) without any convexity assumption. Using the concept of \emph{optimal value function}, we transform the problem into that of solving a nonsmooth system of inequalities. Based on…