We prove the theoretical convergence of a short-step, approximate pathfollowing, interior-point primal-dual algorithm for semidefinite programs based on the Gauss-Newton direction obtained from minimizing the norm of the perturbed optimality conditions. This is the first proof of convergence for the Gauss-Newton direction in this context. It assumes strict complementarity and uniqueness of the ...

The famous Newton–Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton’s method to a solution of an equation. Here we present a “Kantorovich type” convergence analysis for the Gauss–Newton’s method which improves the result in [W.M. Häußler, A Kantorovich-type convergence analysis for the Gauss–Newton-method, Numer. Math. 48 (1986) 119–125...

In this paper we present several Gauss-Newton algorithms for blind source separation of convolutive mixtures. The algorithms can be interpreted as generalizations of two previous approaches due to Gerven-Compernolle [7] and Nguyen-Jutten [5]. Since they are of the Gauss-Newton type, they exhibit a fast rate of convergence. Also, we present a stability analysis for two sources and instantaneous ...

Two trust-region methods for systems of mixed nonlinear equalities, general inequalities and simple bounds are proposed. The first method is based on a Gauss-Newton model, the second one is based on a regularized Gauss-Newton model and results to be a Levenberg-Marquardt method. The globalization strategy uses affine scaling matrices arising in bound-constrained optimization. Global convergence...

We describe regularization tools for training large-scale artiicial feed-forward neural networks. In a companion paper (in this issue) we give the basic ideas and some theoretical results regarding the Gauss-Newton method compared to other methods such as the Levenberg-Marquardt method applied on small and medium size problems. We propose algorithms that explicitly use a sequence of Tikhonov re...

The L-function of a non-degenerate twisted Witt extension is proved to be a polynomial. Its Newton polygon is proved to lie above the Hodge polygon of that extension. And the Newton polygons of the Gauss-Heilbronn sums are explicitly determined, generalizing the Stickelberger theorem.

The problem of this research tackles the process of fitting two concentric spheres to data, which arises in computational metrology. There are also many fitting criteria that could be used effectively, and the most widely used one in metrology, for example, is that of the sum of squared minimal distance. However, a simple and robust algorithm assigned for using the orthogonal distance regressio...

Approximate Newton methods are a standard optimization tool which aim to maintain the benefits of Newton’s method, such as a fast rate of convergence, whilst alleviating its drawbacks, such as computationally expensive calculation or estimation of the inverse Hessian. In this work we investigate approximate Newton methods for policy optimization in Markov decision processes (MDPs). We first ana...