Model predictive control is a receding horizon control policy in which a linear or quadratic program with linear constraints is solved on-line at each sampling instance. An algorithm is developed that allows quick computation of suboptimal control moves. The linear constraint set is approximated by an ellipsoid and a change of variables is performed so that a solution may be computed eciently ...

We present a new batch learning algorithm for text classification in the vector space of document representations. The algorithm uses ellipsoid separation [3] in the feature space which leads to a semidefinite program. An approximation of the latent semantic feature extraction approach using Gram-Schmidt orthogonalization [2] is used for the feature extraction. Preliminary results demonstrate s...

A new exact approach to the stable set problem is presented, which attempts to avoids the pitfalls of existing approaches based on linear and semidefinite programming. The method begins by constructing an ellipsoid that contains the stable set polytope and has the property that the upper bound obtained by optimising over it is equal to the Lovász theta number. This ellipsoid is then used to der...

In this report, we consider the problem of nding the maximum-volume ellipsoid inscribing a given full-dimensional polytope in < n deened by a nite set of aane inequalities. We present several formulations for the problem that may serve as algorithmic frameworks for applying interior-point methods. We propose a practical interior-point algorithm based on one of the formulations and present preli...

Compared to normal learning algorithms, for example backpropagation, the optimal bounded ellipsoid (OBE) algorithm has some better properties, such as faster convergence, since it has a similar structure as Kalman filter. OBE has some advantages over Kalman filter training, the noise is not required to be Guassian. In this paper OBE algorithm is applied traing the weights of recurrent neural ne...

We describe a generalised method for ellipsoid fitting against a minimum set of data points. The proposed method is numerically stable and applies to a wide range of ellipsoidal shapes, including highly elongated and arbitrarily oriented ellipsoids. This new method also provides for the retrieval of rotational angle and length of semi-axes of the fitted ellipsoids accurately. We demonstrate the...

Abstract. We study the problem of computing a (1 + )-approximation to the minimum volume enclosing ellipsoid of a given point set S = {p1, p2, . . . , pn} ⊆ Rd. Based on a simple, initial volume approximation method, we propose a modification of Khachiyan’s first-order algorithm. Our analysis leads to a slightly improved complexity bound of O(nd3/ ) operations for ∈ (0, 1). As a byproduct, our ...

We study the problem of computing a (1 + )-approximation to the minimum volume enclosing ellipsoid of a given point set S = {p, p, . . . , p} ⊆ R. Based on a simple, initial volume approximation method, we propose a modification of Khachiyan’s first-order algorithm. Our analysis leads to a slightly improved complexity bound of O(nd/ ) operations for ∈ (0, 1). As a byproduct, our algorithm retur...

The ellipsoid algorithm is a fundamental for computing solution to the system of m linear inequalities in n variables [Formula: see text] when its set solutions has positive volume. However, infeasible, no mechanism proving that (P) infeasible. This contrast other two algorithms tackling text], namely, simplex and interior-point methods, each which can be easily implemented way either produces ...

This paper describes an ellipsoid algorithm that solves convex problems having linear equality constraints with or without inequality constraints. Experimental results show that the new method is also effective for some problems that have nonlinear equality constraints or are otherwise nonconvex.