We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer memory or data are collected in real-time). In our proposed framework, stochasticity is introduced in two different frameworks as a means to overcome these compu...

With the ultimate goal of iteratively solving piecewise smooth (PS) systems, we consider the solution of piecewise linear (PL) equations. As shown in [Gri13] PL models can be derived in the fashion of automatic or algorithmic differentiation as local approximations of PS functions with a second order error in the distance to a given reference point. The resulting PL functions are obtained quite...

There was a witch in Youghal. l\1ary Longdon testified before the Assize at Cork on 11 September, 1661, that she had been bewitched by Florence Newton. Longdon said Newton, after kissing her on the forehead, had caused her to suffer fits and trances, during which Longdon saw Newton's face and knew that Newton was the cause of her malady. Longdon testified that during her fits she vomited foreig...

A modified version of the truncated-Newton algorithm of Nash ([24], 125], [29]) is presented differing from it only in the use of an exact Hessian vector product for carrying out the large-scale unconstrained optimization required in variational data assimilation. The exact Hessian vector product is obtained by solving an optimal control problem of distributed parameters. (i.e. the system under...

Here, a quasi-Newton algorithm for constrained multiobjective optimization is proposed. Under suitable assumptions, global convergence of the algorithm is established.

In this work, we address the implementation and performance of inexact Newton-Krylov quasi-Newton algorithms, more specifically BFGS method, for solution nonlinear elasticity equations, compare them to a standard method. This is done through systematic analysis solvers with respect problem size, magnitude data number processors in both almost incompressible mechanics. We consider three test cas...