Convergence Order of McCormick Relaxations of LMTD function in Heat Exchanger Networks

Models used in process systems engineering often contain nonconvex and nonlinear functions. In this work we consider the logarithmic mean temperature difference used in heat exchanger networks. Building on the work of Mistry and Misener (2015), we present an approach to construct tight convex and concave relaxations of this function when the temperatures are not degrees of freedom but rather calculated as a function of the optimization variables. We make use of the multivariate McCormick theorem presented by Tsoukalas and Mitsos (2014) and support this approach by a simple case study where we additionally conclude results on the convergence orders of the obtained relaxations. Finally we also briefly compare with other relaxation techniques including interval extensions and α BB relaxations.