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About 3,715 papers for “Ellipsoid method”

Ellipsoid method

Tunçel, Levent · American Mathematical Society eBooks · 2010

Cited by 1

Ellipsoid Method

Steffen Rebennack · Encyclopedia of Optimization · 2008

Cited by 4

The Ellipsoid Method

Martin Grötschel, László Lovász, Alexander Schrijver · Algorithms and combinatorics · 1993

Cited by 38

The ellipsoid method redux

Michael J. Todd · arXiv (Cornell University) · 2023

We reconsider the ellipsoid method for linear inequalities. Using the ellipsoid representation of Burrell and Todd, we show the method can be viewed as coordinate descent on the volume of an enclosing ellipsoid, or on a potential function, or on both. The method can be enhanced by improving the lower bounds generated and by allowing the weights on inequalities to be decreased as well as increased, while still guaranteeing a decrease in volume. Three different initialization schemes are described, and preliminary computational results given. Despite the improvements discussed, these are not encouraging.

Cited by 4Open access

Online learning by ellipsoid method

Liu Yang, Rong Jin, Jieping Ye · 2009

In this work, we extend the ellipsoid method, which was originally designed for convex optimization, for online learning. The key idea is to approximate by an ellipsoid the classification hypotheses that are consistent with all the training examples received so far. This is in contrast to most online learning algorithms where only a single classifier is maintained at each iteration. Efficient algorithms are presented for updating both the centroid and the positive definite matrix of ellipsoid given a misclassified example. In addition to the classical ellipsoid method, an improved version for online learning is also presented. Mistake bounds for both ellipsoid methods are derived. Evaluation with the USPS dataset and three UCI data-sets shows encouraging results when comparing the proposed online learning algorithm to two state-of-the-art online learners.

Cited by 33

New RHT-Based Ellipsoid Recovery Method

Chunguang Cao, Timothy S. Newman · 2006

A new method that enables Randomized Hough Transform (RHT)-based recovery of ellipsoid parameters from a collection of 3D points is presented. The approach is attractive since it can alleviate the traditional Hough Transform’s disadvantages of large computation time and memory usage—in particular for the ellipsoid detection’s highdimensional parameter space. The new method uses two RHT-based stages, first exploiting shape to enable recovery of position and then exploiting eigen analysis to recover the remaining parameters (of shape and orientation). Experimental results on synthetic and real data are also presented.

Cited by 1

ON A MODIFICATION OF ELLIPSOID METHOD

Petro Stetsyuk, Evgeni Nurminski · 2016

A modification of the ellipsoid method (EM) is considered. This modification (MEM) is asymptotically equivalent to the original EM for large-scale problems but applicable to lower dimensions down to one-dimensional case. MEM preserves close to EM volume reduction factors for all dimensions and gives close to optimal 0.5 accuracy improving multiplier for 1d.

Cited by 0

The ellipsoid method with quantum subroutines

Benjamin Hanzsek-Brill, Benjamin Hanzsek-Brill · Summit (Simon Fraser University)

This project begins the process of adapting the ellipsoid method of optimization to use quantum subroutines.It uses Nannicini's Sign Detection Algorithm on quantum states as well as Grover's Search Algorithm to provide substantial speedup in finding a constraint violated by a potential solution for a given LP.In specific, given an LP with an M N constraint matrix and maximum bit length E of a single variable, the complexity of findingwith the quantum subroutine.This is accompanied by computer simulations of the quantum circuit to solve small linear programs.

Cited by 0Open access

The Ellipsoid Method Generates Dual Variables

Bruce P. Burrell, Michael J. Todd · Mathematics of Operations Research · 1985

We show that the ellipsoid algorithm applied to a system of linear inequalities can be implemented in such a way that at each iteration there is a short proof of the containment of the feasible region in the current ellipsoid. Moreover, the data describing each ellipsoid also generate dual variables that provide bounds on the linear functions appearing in the inequalities.

Cited by 22

Lecture 2: LP Duality, Simplex Method Complexity, Ellipsoid Method

Lecturer Pankaj, K. Agarwal, Scribe Sam Slee · 2007

In the last lecture we introduced linear programming, a type of optimization problem in which we have m linear constraints on n variables x1,..., xn and the goal is to either minimize or maximize a linear objective function composed of those variables. To aid our discussion of the problem an example LP in matrix form and a visual example are each given below. maximize: c T x such that: Ax ≤ b xi ≥ 0 ∀ xi ∈ x A: m × n matrix of constraint coefficients x: LP variables c: objective function coefficients b: constraint equation constants 2.1 Linear Programming Duality Figure 2.1: An instance of a 2D linear programming problem. An interesting concept associated with linear programs is that of duality. For every LP problem there is a second LP problem with which it is intrinsically paired. This second LP problem can bound the feasible values of the first problem and even help find the optimal value to that problem. The initial LP problem is called the primal LP while the second is referred to as the dual LP. Consider the example LP problem given below.

Cited by 0

A direct ellipsoid method for linear programming

Shiquan Wu, Fang Wu · Bulletin of the Australian Mathematical Society · 1993

This paper indicates how to apply the ellipsoid method directly to Linear Programming problems and proves that this kind of version of the ellipsoid method is almost as good as Karmarkar's type method in the theoretical sense.

Cited by 1Open access

Subgradient ellipsoid method for nonsmooth convex problems

Anton Rodomanov, Yurii Nesterov · Mathematical Programming · 2022

In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth convex minimization problems, convex-concave saddle-point problems and variational inequalities with monotone operator. Our algorithm can be seen as a combination of the standard Subgradient and Ellipsoid methods. However, in contrast to the latter one, the proposed method has a reasonable convergence rate even when the dimensionality of the problem is sufficiently large. For generating accuracy certificates in our algorithm, we propose an efficient technique, which ameliorates the previously known recipes (Nemirovski in Math Oper Res 35(1):52-78, 2010).

Cited by 14Open access

Homogeneous Control Design Using Invariant Ellipsoid Method

Siyuan Wang, Haibin Duan, Gang Zheng et al. · IEEE Transactions on Automatic Control · 2024

The invariant ellipsoid method is aimed at minimization of the smallest invariant and attractive set of a control system operating under bounded external disturbances and parametric uncertainties. This paper extends this technique to a class of the so-called generalized homogeneous system. The generalized homogeneous optimal (in the sense of invariant ellipsoid) controller allows further improvement of the control system providing a faster convergence and smaller overshoots. Theoretical results are supported by numerical simulations and experiments.

Cited by 5Open access

Homogeneous control design using invariant ellipsoid method

Siyuan Wang, Andrey Polyakov, Gang Zheng et al. · arXiv (Cornell University) · 2023

The invariant ellipsoid method is aimed at minimization of the smallest invariant and attractive set of a linear control system operating under bounded external disturbances. This paper extends this technique to a class of the so-called generalized homogeneous system by defining the $\dn-$homogeneous invariant/attractive ellipsoid. The generalized homogeneous optimal (in the sense of invariant ellipsoid) controller allows further improvement of the control system providing a faster convergence and better precision. Theoretical results are supported by numerical simulations and experiments.

Cited by 0Open access

DESIGN METHOD FOR ISOTENSOID ELLIPSOID SHAPED PRESSURE VESSELS

David Schlegel, Florian Schmidt, Michael Birke et al. · Zenodo (CERN European Organization for Nuclear Research) · 2023

A design method for ellipsoid shaped composite pressure vessels with isotensoid behaviour will be presented

Cited by 0Open access