Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/288621 
Year of Publication: 
2020
Citation: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 80 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2020 [Pages:] 3-29
Publisher: 
Springer US, New York, NY
Abstract: 
It is a challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists. This task can be understood as the inverse problem of multiobjective optimization, where the goal is to find the objective function vector of a given Pareto set. To this end, we present a method to construct the objective function vector of an unconstrained multiobjective optimization problem (MOP) such that the Pareto critical set contains a given set of data points with prescribed KKT multipliers. If such an MOP can not be found, then the method instead produces an MOP whose Pareto critical set is at least close to the data points. The key idea is to consider the objective function vector in the multiobjective KKT conditions as variable and then search for the objectives that minimize the Euclidean norm of the resulting system of equations. By expressing the objectives in a finite-dimensional basis, we transform this problem into a homogeneous, linear system of equations that can be solved efficiently. Potential applications of this approach include the identification of objectives (both from clean and noisy data) and the construction of surrogate models for expensive MOPs.
Subjects: 
Multiobjective optimization
Inverse optimization
Pareto set
Pareto critical set
JEL: 
N45
C29
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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