Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques

This paper has as a major objective to present a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are e...

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Bibliographic Details
Published in:Optimization and engineering Vol. 3; no. 3; pp. 227 - 252
Main Author: Grossmann, Ignacio E.
Format: Journal Article
Language:English
Published: Dordrecht Springer Nature B.V 01.09.2002
Subjects:
Bending machines
Cutting
Derivation
Mathematical analysis
Mathematical models
Nonlinear programming
Nonlinearity
Optimization
Studies
ISSN:1389-4420, 1573-2924
Online Access:Get full text
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Summary:This paper has as a major objective to present a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.[PUBLICATION ABSTRACT]
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ISSN:1389-4420
1573-2924
DOI:10.1023/A:1021039126272