MVE Problem: Maximum Volume Ellipsoid Problem

The Maximum Volume Ellipsoid Problem is to find the largest ellipsoid (measured by volume) inscribing a given polytope defined by a finite number of linear inequalities; that is, Ax <= b, where A is an m by n matrix with m > n and b is an m-vector.

By definition, a polytope is a bounded polyhedron. For the problem to have a meaningful solution, the polytope must be full dimensional (i.e., it must have a non-zero volume).

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Yin Zhang and Liyan Gao. On Numerical Solution of the Maximum Volume Ellipsoid Problem. SIAM Journal on Optimization, Vol.14, No.1, pp. 53-76, 2003.


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