Mixed integer programming with a class of nonlinear convex constraints

We study solution approaches to a class of mixed-integer nonlinear programming problems that arise from recent developments in risk-averse stochastic optimization and contain second- and p-order cone programming as special cases. We explore possible applications of some of the solution techniques th...

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Published in:Discrete optimization Vol. 24; pp. 66 - 86
Main Authors: Vinel, Alexander, Krokhmal, Pavlo A.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.05.2017
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ISSN:1572-5286, 1873-636X
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Abstract We study solution approaches to a class of mixed-integer nonlinear programming problems that arise from recent developments in risk-averse stochastic optimization and contain second- and p-order cone programming as special cases. We explore possible applications of some of the solution techniques that have been successfully used in mixed-integer conic programming and show how they can be generalized to the problems under consideration. Particularly, we consider a branch-and-bound method based on outer polyhedral approximations, lifted nonlinear cuts, and linear disjunctive cuts. Results of numerical experiments with discrete portfolio optimization models are presented.
AbstractList We study solution approaches to a class of mixed-integer nonlinear programming problems that arise from recent developments in risk-averse stochastic optimization and contain second- and p-order cone programming as special cases. We explore possible applications of some of the solution techniques that have been successfully used in mixed-integer conic programming and show how they can be generalized to the problems under consideration. Particularly, we consider a branch-and-bound method based on outer polyhedral approximations, lifted nonlinear cuts, and linear disjunctive cuts. Results of numerical experiments with discrete portfolio optimization models are presented.
Author Vinel, Alexander
Krokhmal, Pavlo A.
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  givenname: Pavlo A.
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  organization: Department of Systems & Industrial Engineering, University of Arizona, 1127 E James E. Rogers Way, Tucson, AZ 85721, USA
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Keywords Measures of risk
Valid inequalities
Mixed-integer nonlinear programming
Conic programming
Quasi-arithmetic average
Language English
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Snippet We study solution approaches to a class of mixed-integer nonlinear programming problems that arise from recent developments in risk-averse stochastic...
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StartPage 66
SubjectTerms Conic programming
Measures of risk
Mixed-integer nonlinear programming
Quasi-arithmetic average
Valid inequalities
Title Mixed integer programming with a class of nonlinear convex constraints
URI https://dx.doi.org/10.1016/j.disopt.2016.07.002
Volume 24
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