50 years of mixed-integer nonlinear and disjunctive programming

This paper gives an overview of the development of Mixed-Integer Nonlinear Programming (MINLP) and Generalized Disjunctive Programming (GDP) over the past fifty years. We cover key methods, algorithms, and techniques for solving MINLPs and GDPs, focusing on both the modeling framework and solution t...

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Bibliographic Details
Published in:European journal of operational research
Main Authors: Kronqvist, Jan, Bernal Neira, David E., Grossmann, Ignacio E.
Format: Journal Article
Language:English
Published: Elsevier B.V 2025
Subjects:
Disjunctive programming
Generalized disjunctive programming
Mixed-integer nonlinear programming
Mixed-integer programming
Outer approximation
Generalized disjunctive programming
Outer approximation
Mixed-integer nonlinear programming
Disjunctive programming
Mixed-integer programming
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:This paper gives an overview of the development of Mixed-Integer Nonlinear Programming (MINLP) and Generalized Disjunctive Programming (GDP) over the past fifty years. We cover key methods, algorithms, and techniques for solving MINLPs and GDPs, focusing on both the modeling framework and solution techniques. We provide historical perspectives, highlight the key features and major challenges, and aim to give an in-depth introduction to the fields. We also discuss some future research directions. The paper is aimed at readers who are familiar with Mixed-Integer Linear Programming but are not experts on MINLP or GDP. •Overview of mixed-integer nonlinear programming.•Overview of generalized disjunctive programming.•Algorithms for MINLP.•Mixed-integer formulations of disjunctive constraints.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2025.07.016