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2013
In this chapter we describe an algorithm, known as the ellipsoid method, that finds a solution to a given system of linear inequalities. Its complexity analysis can also be done in terms of Open image in new window , but in exchange for a loss of simplicity, we obtain bounds linear in Open image in new window (instead of the quadratic dependence in ...
Peter Bürgisser, Felipe Cucker
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In this chapter we describe an algorithm, known as the ellipsoid method, that finds a solution to a given system of linear inequalities. Its complexity analysis can also be done in terms of Open image in new window , but in exchange for a loss of simplicity, we obtain bounds linear in Open image in new window (instead of the quadratic dependence in ...
Peter Bürgisser, Felipe Cucker
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1988
In 1979 a note of L. G. Khachiyan indicated how an algorithm, the so-called ellipsoid method, originally devised for nonlinear nondifferentiable optimization, can be modified in order to check the feasibility of a system of linear inequalities in polynomial time.
Martin Grötschel +2 more
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In 1979 a note of L. G. Khachiyan indicated how an algorithm, the so-called ellipsoid method, originally devised for nonlinear nondifferentiable optimization, can be modified in order to check the feasibility of a system of linear inequalities in polynomial time.
Martin Grötschel +2 more
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An Approximate Method of Ellipsoids
Cybernetics and Systems Analysis, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Ellipsoidal methods for dynamics and control. Part I
Journal of Mathematical Sciences, 2006The system that operates in the absence of uncertainty is considered. Methods that allow one to represent trajectory tubes for control systems by parametrized varieties of ellipsoid-valued tubes are proposed. They allow one to obtain external and internal approximation of the multivalued solution functions with any desired accuracy.
P. Varaiya +2 more
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Variable metric relaxation methods, part II: The ellipsoid method
Mathematical Programming, 1984[For part I see Tech. Rep. SOL 81-16, Systems Optimization Laboratory, Oper. Res. Dept., Stanford Univ. (1981).] The deepest, or least shallow, cut ellipsoid method is a polynomial (time and space) method which finds an ellipsoid, representable by polynomial space integers, such that the maximal ellipsoidal distance relaxation method using this fixed ...
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Die Ellipsoid-Methode von Chatschijan
1987Das Verfahren von Chatschijan arbeitet mit einer Folge von Ellipsoiden fallenden Volumens, die die moglichen Optimalpunkte einer linearen Optimierungsaufgabe sukzessive einschliesen. Die Grundidee des Verfahrens wird erlautert an einem Verfahren zur Ermittlung zulassiger Punkte.
Ernst-Peter Beisel, Manfred Mendel
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Minimax estimation methods under ellipsoidal constraints
Automation and Remote Control, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mamaev, A. A., Semenikhin, K. V.
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Attractive Ellipsoid Method with Adaptation
2014This chapter deals with the development of a state estimator and adaptive controller based on the attractive ellipsoid method (AEM) for a class of uncertain nonlinear systems having “quasi-Lipschitz” nonlinearities as well as external perturbations.
Alexander Poznyak +2 more
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On a Variant of the Ellipsoid Method: Using Simplices instead of Ellipsoids
1996The ellipsoid method finds an optimal solution (if one exists) of a linear programming problem. Khachiyan showed that the running time of the algorithm is bounded from above by a fixed polynomial in the size of the data. From a theoretical point of view this result was very important.
Faigle, U. +2 more
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New RHT-Based Ellipsoid Recovery Method
18th International Conference on Pattern Recognition (ICPR'06), 2006A 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 high-dimensional ...
null Chunguang Cao, T.S. Newman
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