Let \calS denote the convex hull of m full-dimensional ellipsoids in R^n. Given ϵ>0 and δ>0,
we study the problems of computing a (1+ϵ)-approximation to the minimum volume covering
ellipsoid of \calS and a (1+δ)n-rounding of \calS. We extend the first-order algorithm of
Kumar and J. Optim. Theory Appl., 126 (2005), pp. 1–21 that computes an approximation to
the minimum volume covering ellipsoid of a finite set of points in R^n, which, in turn, is a
modification of Khachiyan's algorithm LG Khachiyan, Math. Oper. Res., 21 (1996), pp. 307 …

Let S denote the convex hull of m full-dimensional ellipsoids in ℝn. Given ε> 0 and δ> 0, we
study the problems of computing a (1+ ε)-approximation to the minimum volume covering
ellipsoid of S and a (1+ δ) n-rounding of S. We extend the first-order algorithm of Kumar and
Yildirim [J. Optim. Theory Appl., 126 (2005), pp. 1-21] that computes an approximation to the
minimum volume covering ellipsoid of a finite set of points in ℝn, which, in turn, is a
modification of Khachiyan's algorithm [LG Khachiyan, Math. Oper. Res., 21 (1996), pp. 307 …