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Publication . Article . 2012

Non-convex mixed-integer nonlinear programming: A survey

Samuel Burer; Adam N. Letchford;
Open Access
Published: 01 Jul 2012 Journal: Surveys in Operations Research and Management Science, volume 17, pages 97-106 (issn: 1876-7354, Copyright policy )
Publisher: Elsevier BV
Country: United Kingdom
Abstract

Abstract A wide range of problems arising in practical applications can be formulated as Mixed-Integer Nonlinear Programs (MINLPs). For the case in which the objective and constraint functions are convex, some quite effective exact and heuristic algorithms are available. When non-convexities are present, however, things become much more difficult, since then even the continuous relaxation is a global optimization problem. We survey the literature on non-convex MINLPs, discussing applications, algorithms, and software. Special attention is paid to the case in which the objective and constraint functions are quadratic.

Subjects by Vocabulary

Microsoft Academic Graph classification: Mathematics Nonlinear mixed integer programming Regular polygon Mathematical optimization Nonlinear system Range (mathematics) Heuristic (computer science) Relaxation (approximation) Software business.industry business Quadratic equation

Subjects

Management Science and Operations Research, Computer Science Applications, Economics and Econometrics, Information Systems, HB Economic Theory

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