---
res:
bibo_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.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Bennet
foaf_name: Gebken, Bennet
foaf_surname: Gebken
foaf_workInfoHomepage: http://www.librecat.org/personId=32643
- foaf_Person:
foaf_givenName: Sebastian
foaf_name: Peitz, Sebastian
foaf_surname: Peitz
foaf_workInfoHomepage: http://www.librecat.org/personId=47427
orcid: https://orcid.org/0000-0002-3389-793X
bibo_doi: 10.1007/s10898-020-00983-z
bibo_volume: 80
dct_date: 2021^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: 'Inverse multiobjective optimization: Inferring decision criteria from
data@'
...