Modular neural networks use a single gating neuron to select the outputs of a collection of agent neurons. Expectation-maximization (EM) algorithms provide one way of training modular neural networks to approximate non-linear functionals. This paper introduces a hybrid interior-point (HIP) algorithm for training modular networks. The HIP algorithm combines an interior-point linear programming (...

Traditional simplex-basedalgorithms for two-stage stochastic linear programscan be broadly divided into two classes: (a) those that explicitly exploit the structure of the equivalent large-scale linear program and (b) those based on cutting planes (or equivalently on decomposition) that implicitly exploit that structure. Algorithms of class (b) are in general preferred. In 1988, following the w...

In this article we consider modiied search directions in the endgame of interior point methods for linear programming. In this stage, the normal equations determining the search directions become ill-conditioned. The modiied search directions are computed by solving perturbed systems in which the systems may be solved ef-ciently by the preconditioned conjugate gradient solver. We prove the conv...

In this paper we continue the development of a theoretical foundation for efficient primal-dual interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are self-scaled (see [NT97]). The class of problems under consideration includes linear programming, semidefinite programming and convex quadratically constrained quadratic prog...

Two Primal-dual interior point algorithms are presented for the problem of maximizing the smallest eigenvalue of a symmetric matrix over diagonal perturbations. These algorithms prove to be simple, robust, and eecient. Both algorithms are based on transforming the problem to one over the cone of positive semideenite matrices. One of the algorithms does this transformation through an intermediat...

A sphere excited by an interior point source or a point dipole gives a simplified yet realistic model for studying a variety of applications in medical imaging. We suppose that there is an exterior field (transmission problem) and that the total field on the sphere is known. We give analytical inversion algorithms for determining the interior physical characteristics of the sphere as well as th...

A generalized class of infeasible-interior-point methods for solving horizontal linear complementarity problem is analyzed and suucient conditions are given for the convergence of the sequence of iterates produced by methods in this class. In particular it is shown that the largest step path following algorithms generates convergent iterates even when starting from infeasible points. The comput...

Based on extensive computational evidence (hundreds of thousands of randomly generated problems) the second author conjectured that κ̄(ζ) = 1 (Conjecture 5.1 in [1]), which is a factor of √ 2n better than has been proved in [1], and which would yield an O( √ n) iteration full-Newton step infeasible interior-point algorithm. In this paper we present an example showing that κ̄(ζ) is in the order of...

We present ellipsoid algorithms for convexly constrained estimation and design problems. The proposed polynomial time algorithms yield both an estimate of the complete set of feasible solutions and a point estimate in the interior. Optimal cutting hyperplanes are derived, and a computation-ally eecient sequential cut algorithm is proven to provide estimation performance achieving the best exist...