Argonne National Laboratory

Applications and Algorithms for Mixed Integer Nonlinear Programming

TitleApplications and Algorithms for Mixed Integer Nonlinear Programming
Publication TypeConference Paper
Year of Publication2009
AuthorsLeyffer, S, Linderoth, JT, Luedtke, J, Miller, A, Munson, TS
Conference NameJournal of Physics: Conference Series
Date Published04/2009
Other NumbersANL/MCS-P1630-0509

The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Discrete decision variables model dichotomies, discontinuities, and general logical relationships. Nonlinear functions are required to accurately represent physical properties such as pressure, stress, temperature, and equilibrium. Problems involving both discrete variables and nonlinear constraint functions are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems faced by researchers and practitioners. In this paper, we describe relevant scienti c applications that are naturally modeled as MINLPs, we provide an overview of available algorithms and software, and we describe ongoing methodological advances for solving MINLPs. These algorithmic advances are making increasingly larger instances of this important family of problems tractable.