Approximating convex quadratic programming is P-complete

Abstract

In this paper we show that the problem of Approximating Convex Quadratic Programming is P-complete. We also consider two approximation problems related to it, Solution Approximation and Value Approximation and show both of these are P-complete. On the other hand, we show that we can approximate in NC those instances of Quadratic Programming (QP) that are "smooth" and "positive". Finally, we present a problem called Product Arrangement of a graph that is similar to Linear Arrangement. We formulate it as a Positive QP and prove that there is an NCAS for those instances that are "dense".