A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
On the complexity of approximating the maximal inscribed ellipsoid for a polytope
Mathematical Programming: Series A and B
Rounding of polytopes in the real number model of computation
Mathematics of Operations Research
Fast training of support vector machines using sequential minimal optimization
Advances in kernel methods
Bounding ellipsoids for ray-fractal intersection
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Computation of Minimum-Volume Covering Ellipsoids
Operations Research
On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
Discrete Applied Mathematics
Optimization Methods & Software
Modified algorithms for the minimum volume enclosing axis-aligned ellipsoid problem
Discrete Applied Mathematics
A study on SMO-type decomposition methods for support vector machines
IEEE Transactions on Neural Networks
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We consider the problem of computing a (1+驴)-approximation to the minimum volume enclosing ellipsoid (MVEE) of a given set of m points in R n . Based on the idea of sequential minimal optimization (SMO) method, we develop a rank-two update algorithm. This algorithm computes an approximate solution to the dual optimization formulation of the MVEE problem, which updates only two weights of the dual variable at each iteration. We establish that this algorithm computes a (1+驴)-approximation to MVEE in O(mn 3/驴) operations and returns a core set of size O(n 2/驴) for 驴驴(0,1). In addition, we give an extension of this rank-two update algorithm. Computational experiments show the proposed algorithms are very efficient for solving large-scale problem with a high accuracy.