 
Summary: On the accuracy of approximating a class of
NPcomplete quadratic programs (QP) by a
class of polynomially bounded linear
programs (LP)
M. Vaziri 1
, Student Member IEEE K. A. Ariyawansa 2
K. Tomsovic1
, Senior Member IEEE A. Bose3
, Fellow IEEE
Abstract: In this note we propose a class of linear programming (LP) problems that may be used to approximate
a class of quadratic programming (QP) problems that arise in some engineering related applications in
particular here for the electric power system distribution expansion planning. We then derive an estimate on the
QP optimum that may be computed using only the solution to the LP. Our approximating LP and the accuracy
estimate are particularly useful for any network flow model such as the distribution expansion problem, where
the QP is proven NPComplete while LP is polynomially bounded. Although our derivation is valid for QP
models more general than the network flow models of interest to us, we describe the latter as well in our note
since that motivated us to derive our estimate. We also report results of some computational experiments
involving instances of these network flow models. The results indicate that the accuracy estimate is sharp and
that the proposed approximating LP is accurate in practice.
Index TermsQuadratic Programming, Power distribution system expansion planning, Linear Programming,
