Year: 2009
Type: conference-paper
Abstract: 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 scientific 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.
Authors: Sven Leyffer, Jeff Linderoth, James Luedtke, Andrew Miller, Todd Munson
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Awards: G222768804, G2287611682, Collaborative Research: Next Generation Solvers for Mixed Integer Nonlinear Programs: Structure, Search, and Implementation, G262962599, G498139845, G513797252, G5398989114, NEXT GENERATION SOLVERS FOR MIXED INTGER NONLINEAR PROGRAMS: STRUCTURE, SEARCH AND IMPLEMENTATION, NEXT GENERATION SOLVERS FOR MIXED INTGER NONLINEAR PROGRAMS: STRUCTURE, SEARCH AND IMPLEMENTATION, G6848031779, G6918803902, OPTIMIZATION UNDER NONCONVEXITY AND UNCERTAINTY: ALGORITHMS AND SOFTWARE, OPTIMIZATION UNDER NONCONVEXITY AND UNCERTAINTY: ALGORITHMS AND SOFTWARE, G878601127, G969889393, G993149817
OpenAlex ID: W2095476732