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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Veröffentlicht in:	Discrete optimization Jg. 24; S. 66 - 86
Hauptverfasser:	Vinel, Alexander, Krokhmal, Pavlo A.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Elsevier B.V 01.05.2017
Schlagworte:	Conic programming Measures of risk Mixed-integer nonlinear programming Quasi-arithmetic average Valid inequalities Measures of risk Valid inequalities Mixed-integer nonlinear programming Conic programming Quasi-arithmetic average
ISSN:	1572-5286, 1873-636X
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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.
ISSN:	1572-5286 1873-636X
DOI:	10.1016/j.disopt.2016.07.002