For a one-parameter deformation of an analytic complex function germ of several variables, there is defined its monodromy zeta-function. We give a Varchenko type formula for this zeta-function if the deformation is non-degenerate with respect to its Newton diagram.

A new and highfy efficient algorithm for nonlinear minimax optimization is presented. The algorithm, based on the work of Hald and Madsen, combines linear programming methods with quasi-Newton methods and has sure convergence properties. A critical review of the existing minimax algorithms is given, and the relation of the qnasi-Newton iteration of the algorithm to the Powell method for rstssdi...

Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if it is hard to approximate the Hessian well and efficiently. As far as we know, there is no effective way to handle this problem. In this paper, we resort to N...

An efficient multi-block Newton–Krylov algorithm using the compressible Navier–Stokes equations is presented for the analysis and design of high-lift airfoil configurations. The preconditioned generalized minimum residual (GMRES) method is applied to solve the discreteadjoint equation, leading to a fast computation of accurate objective function gradients. Furthermore, the GMRES method is used ...

The classical Newton iteration method for matrices can be modified into an efficient algorithm when structured matrices are involved. The difficulty, however, is the importance of the choice of the starting matrix. In this paper, we propose a new initial iteration step which makes the choice of the starting matrix less critical. The validity of the approach is illustrated by numerical experiments.

Abstract. We study the local behavior of a primal-dual inexact interior point methods for solving nonlinear systems arising from the solution of nonlinear optimization problems or more generally from nonlinear complementarity problems. The algorithm is based on the Newton method applied to a sequence of perturbed systems that follows by perturbation of the complementarity equations of the origi...

Most existing methods for calculating the steady state solution of the lattice Boltzmann equations are based on pseudo time stepping, which often requires a large number of time steps especially for high Reynolds number problems. To calculate the steady state solution directly without the time integration, in this paper we propose and study a nonlinearly preconditioned inexact Newton algorithm ...

The multiplicative Newton-like method developed by the author et al. is extended to the situation where the dynamics is restricted to the orthogonal group. A general framework is constructed without specifying the cost function. Though the restriction to the orthogonal groups makes the problem somewhat complicated, an explicit expression for the amount of individual jumps is obtained. This algo...

Recent efforts in differentiable non-linear programming have been focused on interior point methods, akin to penalty and barrier algorithms. In this paper, we address the classical equality constrained program solved using the simple quadratic loss penalty function/algorithm. The suggestion to use extrapolations to track the differentiable trajectory associated with penalized subproblems goes b...

We present a Gauss-Newton-on-manifold approach for estimating the relative pose (position and orientation) between a 3D object and its projection on a 2D image plane from a set of point correspondences. The pose estimation problem is formulated as an optimization over three rotation parameters on the intersection of the manifold of the rotation matrices and a cone constraint on these matrices t...