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1.1 Pseudocode of Ellipsoid Algorithm Algorithm 1.1 (Ellipsoid Algorithm).
, 2005
"... Summary: In the spring of 1979, the Soviet mathematician L.G.Khachian discovered a polynomial algorithm for LP called Ellipsoid Algorithm. This discovery classifies the linear programming problem in class P for the first time. After the high level introduction of the algorithm in the last class, we ..."
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Summary: In the spring of 1979, the Soviet mathematician L.G.Khachian discovered a polynomial algorithm for LP called Ellipsoid Algorithm. This discovery classifies the linear programming problem in class P for the first time. After the high level introduction of the algorithm in the last class, we
Bounding Ellipsoid Algorithms
"... an attractive alternative to traditional least squares methods for identification and filtering problems involving affineinparameters signal and system models. The benefits – including low computational efficiency, superior tracking ability, and selective updating that permits processor multitask ..."
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tasking – are enhanced by multiweight (MW) optimization in which the data history is considered in determining update times and optimal weights on the observations. MW optimization for OBE algorithms is introduced, and an example MWOBE algorithm implementation is developed around the recent quasiOBE algorithm
A new proof of the ellipsoid algorithm
, 2011
"... Linear programming is described by Howard Karloff as “the process of minimizing a linear objective function, subject to a finite number of linear equality and inequality constraints”. Linear optimization is one of the main tools used in applied mathematics and economics. It finds applications in fi ..."
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programs, the Ellipsoid Algorithm (see [13] for the first appearance). The algorithm is based on the geometry of ellipsoids and how a sequence of progressively smaller ellipsoids contains convex sets. Its ability to run in polynomialtime makes the Ellipsoid Algorithm an important theoretical tool that can
An Interior Ellipsoid Algorithm for Fixed Points
, 1998
"... We consider the problem of approximating fixed points of nonsmooth contractive functions with using of the absolute error criterion. In [12]we proved that the upper bound on the number of function evaluations to compute "approximations is O(n +ln n)) in the worstcase, where 0 !q!1 is t ..."
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Cited by 1 (1 self)
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is the contraction factor and n is the dimension of the problem. This upper bound is achieved by the circumscribed ellipsoid (CE) algorithm combined with a dimensional deflation process. In this paper we present an inscribed ellipsoid (IE) algorithm that enjoys O(n +lnn)) bound. Therefore the IE algorithm has
An Ellipsoid Algorithm for EqualityConstrained Nonlinear Programs
"... 18 Aug 99 Scope and Purpose The purpose of this paper is to present a variant of the ellipsoid algorithm that can be used with equalities. This is a significant improvement over the classical algorithm, which yields accurate solutions to convex and many nonconvex nonlinear programming problems but ..."
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18 Aug 99 Scope and Purpose The purpose of this paper is to present a variant of the ellipsoid algorithm that can be used with equalities. This is a significant improvement over the classical algorithm, which yields accurate solutions to convex and many nonconvex nonlinear programming problems
An ellipsoid algorithm for probabilistic robust controller design
 System and Control Lettets
, 2003
"... Abstract In this paper, a new iterative approach to probabilistic robust controller design is presented, which is applicable to any robust controller/ÿlter design problem that can be represented as an LMI feasibility problem. Recently, a probabilistic Subgradient Iteration algorithm was proposed fo ..."
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Cited by 16 (1 self)
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of possible correction steps, that can be performed by the algorithm before ÿnding a feasible solution, is derived. A method for ÿnding an initial ellipsoid containing the solution set, which is necessary for initialization of the optimization, is also given. The proposed approach is illustrated on a real
A NEW POLYNOMIALTIME ALGORITHM FOR LINEAR PROGRAMMING
 COMBINATORICA
, 1984
"... We present a new polynomialtime algorithm for linear programming. In the worst case, the algorithm requires O(tf'SL) arithmetic operations on O(L) bit numbers, where n is the number of variables and L is the number of bits in the input. The running,time of this algorithm is better than the ell ..."
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Cited by 860 (3 self)
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the ellipsoid algorithm by a factor of O(n~'~). We prove that given a polytope P and a strictly interior point a E P, there is a projective transformation of the space that maps P, a to P', a ' having the following property. The ratio of the radius of the smallest sphere with center a
2010b. Sorting under partial information (without the ellipsoid algorithm
 In STOC ’10: Proceedings of the 42nd ACM symposium on Theory of computing
"... We revisit the wellknown problem of sorting under partial information: sort a finite set given the outcomes of comparisons between some pairs of elements. The input is a partially ordered set P, and solving the problem amounts to discovering an unknown linear extension of P, using pairwise comparis ..."
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Cited by 3 (1 self)
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polynomialtime algorithm for the problem achieving this bound up to a constant factor. Their algorithm invokes the ellipsoid algorithm at each iteration for determining the next comparison, making it impractical. We develop efficient algorithms for sorting under partial information. Like Kahn and Kim, our
Tracking of TimeVarying Parameters using Optimal Bounding Ellipsoid Algorithms
 Proc., 34th Annual Allerton Conf. Communication, Control and Computing, University of Illinois, UrbanaChampaign, Oct 24
, 1996
"... This paper analyzes the performance of an optimal bounding ellipsoid (OBE) algorithm for tracking timevarying parameters with incrementally bounded time variations. A linear statespace model is used, with the timevarying parameters represented by the state vector. The OBE algorithm exhibits a sel ..."
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Cited by 6 (5 self)
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This paper analyzes the performance of an optimal bounding ellipsoid (OBE) algorithm for tracking timevarying parameters with incrementally bounded time variations. A linear statespace model is used, with the timevarying parameters represented by the state vector. The OBE algorithm exhibits a
Results 1  10
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