In applying the level-set method developed in [Van den Berg and Friedlander, SIAM J. on Scientific Computing, 31 (2008), pp. 890–912 and SIAM J. on Optimization, 21 (2011), pp. 1201– 1229] to solve the fused lasso problems, one needs to solve a sequence of regularized least squares subproblems. In order to make the level-set method practical, we develop a highly efficient inexact semismooth New...

The generalized Nash equilibrium is a Nash game, where not only the players’ cost functions, but also the constraints of a player depend on the rival players decisions. We present a globally convergent algorithm that is suited for the computation of a normalized Nash equilibrium in the generalized Nash game with jointly convex constraints. The main tool is the regularized Nikaido-Isoda function...

We present an implicit immersed boundary method for the incompressible Navier–Stokes equations capable of handling three-dimensional membrane–fluid flow interactions. The goal of our approach is to greatly improve the time step by using the Jacobian-free Newton–Krylov method (JFNK) to advance the location of the elastic membrane implicitly. The most attractive feature of this Jacobian-free appr...

This paper examines the e ectiveness of using a quasi-Newton based training of a feedforward neural network for forecasting. We have developed a novel quasi-Newton based training algorithm using a generalized logistic function. We have shown that a well designed feed forward structure can lead to a good forecast without the use of the more complicated feedback/feedforward structure of the recur...

For solving the generalized equation f(x) + F (x) 3 0, where f is a smooth function and F is a set-valued mapping acting between Banach spaces, we study the inexact Newton method described by (f(xk) + Df(xk)(xk+1 − xk) + F (xk+1)) ∩Rk(xk, xk+1) 6 = ∅, where Df is the derivative of f and the sequence of mappings Rk represents the inexactness. We show how regularity properties of the mappings f +...

This paper is devoted to the study of the proximal point algorithm for solving monotone second-order cone complementarity problems. The proximal point algorithm is to generate a sequence by solving subproblems that are regularizations of the original problem. After given an appropriate criterion for approximate solutions of subproblems by adopting a merit function, the proximal point algorithm ...

To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible decomposition of a variety is typically understood in affine space, including also those components with zero coordinates. For the problem of computing solution sets...

A new method for computing the approximation of bivariate matrix function is introduced. It uses the construction of bivariate Newton-Thiele type matrix rational interpolants on a rectangular grid.The rational interpolant is of the formmotivated by Tan and Fang (2000), which is combined by Newton interpolant and branched continued fractions, with scalar denominator. The matrix quotients are bas...

We present a multi-grid method for a class of structured generalized Lya-punov matrix equations. Such equations need to be solved in each step of the Newton method for algebraic Riccati equations, which arise from linear-quadratic optimal control problems governed by partial diierential equations. We prove the rate of convergence of the two-grid method to be bounded independent of the dimension...

We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that the algorithm has super-linear convergence with exponentially high probability, with convergence and complexity guarantees that are independent of condition nu...