Inner approximations of completely positive reformulations of mixed binary quadratic programs: a unified analysis

Every quadratic programming problem with a mix of continuous and binary variables can be equivalently reformulated as a completely positive optimization problem, that is, a linear optimization problem over the convex but computationally intractable cone of completely positive matrices. In this paper...

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Vydané v:Optimization methods & software Ročník 32; číslo 6; s. 1163 - 1186
Hlavný autor: Yildirim, E Alper
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Abingdon Taylor & Francis 02.11.2017
Taylor & Francis Ltd
Predmet:
Approximation
completely positive cone
Continuity (mathematics)
Equivalence
Feasibility
inner approximation
Mathematical programming
mixed binary quadratic programming problems
Optimization
polyhedral approximations
Quadratic programming
ISSN:1055-6788, 1029-4937
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Popis
Shrnutí:Every quadratic programming problem with a mix of continuous and binary variables can be equivalently reformulated as a completely positive optimization problem, that is, a linear optimization problem over the convex but computationally intractable cone of completely positive matrices. In this paper, we focus on general inner approximations of the cone of completely positive matrices on instances of completely positive optimization problems that arise from the reformulation of mixed binary quadratic programming problems. We provide a characterization of the feasibility of such an inner approximation as well as the optimal value of a feasible inner approximation. In particular, our results imply that polyhedral inner approximations are equivalent to a finite discretization of the feasible region of the original completely positive optimization problem. Our characterization yields, as a byproduct, an upper bound on the gap between the optimal value of an inner approximation and that of the original instance. We discuss the implications of this error bound for standard and box-constrained quadratic programs as well as general mixed binary quadratic programs with a bounded feasible region.
Bibliografia:ObjectType-Article-1
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content type line 14
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2016.1245732