ON A CERTAIN PARAMETER OF THE DISCRETIZED EXTENDED LINEAR-QUADRATIC PROBLEM OF OPTIMAL-CONTROL

The number gamma := parallel to (Q) over cap(-1/2) <(RP)over cap>(-1/2 )parallel to is an important parameter for the extended linear-quadrat ic programming (ELQP) problem associated with the Lagrangian L((u) ove r cap, (v) over cap) = (p) over cap .(u) over cap + 1/2 (u) over cap . (P) over cap (u) over cap + (q) over cap .(v) over cap - 1/2 (v) over cap .(R) over cap (u) over cap - (v) over cap .(R) over cap (u) over c ap over polyhedral sets (U) over cap x (V) over cap. Some fundamental properties of the problem, as well as the convergence rates of certain newly developed algorithms for large-scale ELQP, are all related to g amma. In this paper, we derive an estimate of gamma for the ELQP probl ems resulting from discretization of an optimal control problem. We pr ove that the parameter gamma of the discretized problem is bounded ind ependently of the number of subintervals in the discretization.