The radius of the outer Dikin ellipsoid intersection m ellipsoids due to Fu et al. (J. Comb. Optim., 2, 29-50, 1998) is corrected from $$\sqrt{m^2+m}$$ . approximation bound for general convex quadratic constrained nonconvex program correspondingly corrected.

In this paper we study the problem of parametric minimization of convex piecewise quadratic functions. Our study provides a unifying framework for convex parametric quadratic and linear programs. Furthermore, it extends parametric programming algorithms to problems with piecewise quadratic cost functions, paving the way for new applications of parametric programming in dynamic programming and o...

We follow the popular approach for unconstrained minimization, i.e. we develop a local quadratic model at a current approximate minimizer in conjunction with a trust region. We then minimize this local model in order to nd the next approximate minimizer. Asymptot-ically, nding the local minimizer of the quadratic model is equivalent to applying Newton's method to the stationarity condition. For...