Abstract This article studies Gauss–Newton-type methods for over-determined systems to find solutions bilevel programming problems. To proceed, we use the lower-level value function reformulation of programs and consider necessary optimality conditions under appropriate assumptions. First, strict complementarity upper- feasibility constraints, prove convergence a method in computing points sati...

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...

We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a nonresonant complex rank one local system. Aomoto and Kita determined this GaussManin connection for arrangements in general position. We use their results and an algorithm constructed in this paper to determine this Gauss-Manin connection for all arrangements.

We give a uniform short proof of the fact that the intersection of every non-central conjugacy class in a Chevalley group and a big Gauss cell is non-empty and that this intersection contains elements with any prescribed semisimple part. The interest in this property stems at least in part from its relation to Ore's and Thompson's conjectures in the theory of nite groups.

Here is a proof for the demeaning method used in lfe, and a description of the methods used for solving the residual equations. As well as a toy-example. This is a preliminary version of [3]. This method, formulated as the Gauss-Seidel algorithm, was noted in [4] without the author noticing it in the first version of this paper.

In this paper we show some properties of the Newton polygon of a polynomial ordinary differential equation. We give the relation between the Newton polygons of a differential polynomial and its partial derivatives. Newton polygons of evaluations of differential polynomials are also described.

The Newton radius of a code is the largest weight of a uniquely correctable error. We establish a lower bound for the Newton radius in terms of the rate. In particular we show that in any family of linear codes of rate below one half, the Newton radius increases linearly with the codeword length.

Two sets of conditions are presented for the compactness of a real plane algebraic curve, one sufficient and one necessary, in terms of the Newton polygon of the defining polynomial.

Based on the generalized Gauss±Newton method, a new algorithm to minimize the objective function of the penalty method in (Bentley LR. Adv Wat Res 1993;14:137±48) for inverse problems of steady-state aquifer models is proposed. Through detailed analysis of the ``built-in'' but irregular weighting e€ects of the coecient matrix on the residuals on the discrete governing equations, a so-called sc...

We present a sparse Gauss-Newton solver for accelerated sensitivity analysis with applications to wide range of equilibrium-constrained optimization problems. Dense solvers have shown promising convergence rates inverse problems, but the cost assembling and factorizing associated matrices has so far been major stumbling block. In this work, we show how dense Hessian can be transformed into an e...