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Non-Convex Mixed-Integer Nonlinear Programming: A Survey

Samuel Burer (samuel-burer***at***uiowa.edu)
Adam Letchford (a.n.letchford***at***lancaster.ac.uk)

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 optimisation problem. We survey the literature on non-convex MINLP, discussing applications, algorithms and software. Special attention is paid to the case in which the objective and constraint functions are quadratic.

Keywords: mixed-integer nonlinear programming, global optimisation, quadratic programming, polynomial optimisation mixed-integer nonlinear programming, global optimi- sation, quadratic programming, polynomial optimisation

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Global Optimization

Category 3: Integer Programming ((Mixed) Integer Linear Programming )

Citation: S. Burer & A.N. Letchford (2012) Non-convex mixed-integer nonlinear programming: a survey. Surveys in Oper. Res. and Mgmt. Sci., 17, 97-106.

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Entry Submitted: 02/29/2012
Entry Accepted: 02/29/2012
Entry Last Modified: 09/05/2012

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