Summary: The number \(\gamma:= |\widehat Q^{-{1\over 2}} \widehat R\widehat P^{- {1\over 2}}|\) is an important parameter for the extended linear-quadratic programming (ELQP) problem associated with the Lagrangian \(L(\widehat u, \widehat v)= \widehat p\cdot \widehat u+ {1\over 2} \widehat u\cdot \widehat P \widehat u+ \widehat q\cdot \widehat v- {1\over 2} \widehat v\cdot \widehat Q \widehat v- \widehat v\cdot \widehat R\widehat v\) over polyhedral sets \(\widehat U\times \widehat V\). 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 \(\gamma\).
In this paper, we derive an estimate of \(\gamma\) for the ELQP problems resulting from discretization of an optimal control problem. We prove that the parameter \(\gamma\) of the discretized problem is bounded independently of the number of subintervals in the discretization.