Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/287278 
Year of Publication: 
2021
Citation: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 82 [Issue:] 3 [Publisher:] Springer US [Place:] New York, NY [Year:] 2021 [Pages:] 615-626
Publisher: 
Springer US, New York, NY
Abstract: 
In a single-objective setting, nonconvex quadratic problems can equivalently be reformulated as convex problems over the cone of completely positive matrices. In small dimensions this cone equals the cone of matrices which are entrywise nonnegative and positive semidefinite, so the convex reformulation can be solved via SDP solvers. Considering multiobjective nonconvex quadratic problems, naturally the question arises, whether the advantage of convex reformulations extends to the multicriteria framework. In this note, we show that this approach only finds the supported nondominated points, which can already be found by using the weighted sum scalarization of the multiobjective quadratic problem, i.e. it is not suitable for multiobjective nonconvex problems.
Subjects: 
Multiobjective optimization
Completely positive optimization
Quadratic programming
Convexification
JEL: 
B48
C29
C20
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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