In this paper we survey some results concerning polynomial and/or strongly polynomial solvability of some classes of quadratic programming problems. The discussion on polynomial solvability of continuous convex quadratic programming is followed by a couple of models for quadratic integer programming which, due to their special structure, allow polynomial (or even strongly polynomial) solvabilit...

We consider convex quadratic programming problem with convex quadratic constraints and suggest a modification of the well-known ellipsoid method based on using an ellipsoidal layer in the problem of circumscribing the minimum volume ellipsoid around of a part of a given ellipsoid. Our paper contains further development and improvement of the technique previously developed in [E.G88]. We show ho...

Well{posedness of a constant{coeecient, rst{order, hyperbolic system is equivalent to the existence of a symmetrizer. This symmetrizer is usually constructed in Fourier space and generally depends on the wave number. Nevertheless, many physical systems have constant symmetrizers which deene a quadratic entropy. This paper presents physically relevant systems with relaxation which are stiiy well...

Newton’s algorithm and some of its variations are often used to find global minima of real valued functions. We propose another such variation and prove its local quadratic convergence. We combine this with Armijo type line search method to produce global convergence, which is eventually quadratic, for the important class of strictly convex functions. Computational performance on some standard ...

In this paper, we focus on the application of the Peaceman-Rachford splitting method (PRSM) to a convex minimization model with linear constraints and a separable objective function. Compared to the Douglas-Rachford splitting method (DRSM), another splitting method from which the alternating direction method of multipliers originates, PRSM requires more restrictive assumptions to ensure its con...