This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.
R. Schöne. T. Hanning. "Least Squares Problems with Absolute Quadratic Constraints." J. Appl. Math. 2012 1 - 12, 2012. https://doi.org/10.1155/2012/312985