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→Constructing loss and objective functions: convert to citeq |
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In many applications, objective functions, including loss functions as a particular case, are determined by the problem formulation. In other situations, the decision maker’s preference must be elicited and represented by a scalar-valued function (called also [[utility]] function) in a form suitable for optimization — the problem that [[Ragnar Frisch]] has highlighted in his Nobel Prize lecture.<ref>{{cite book| first=Ragnar|last=Frisch|date=1969 |title= The Nobel Prize–Prize Lecture|chapter=From utopian theory to practical applications: the case of econometrics|url=https://www.nobelprize.org/prizes/economic-sciences/1969/frisch/lecture/|access-date=15 February 2021}}</ref>
The existing methods for constructing objective functions are collected in the proceedings of two dedicated conferences.<ref name="TangianGruber1997">{{citeq|Q130238799}}</ref><ref name="TangianGruber2002">{{Citeq|Q130238809}}</ref>
In particular, [[Andranik Tangian]] showed that the most usable objective functions — quadratic and additive — are determined by a few indifference points. He used this property in the models for constructing these objective functions from either [[ordinal utility|ordinal]] or [[cardinal utility|cardinal]] data that were elicited through computer-assisted interviews with decision makers.<ref name="Tangian2002">{{Citeq|Q130238814}}</ref><ref name="Tangian2004additiveUtility">{{
Among other things, he constructed objective functions to optimally distribute budgets for 16 Westfalian universities<ref name="Tangian2004universityBudgets">{{Cite journal |last=Tangian |first=Andranik |year=2004 |title= Redistribution of university budgets with respect to the status quo |journal= European Journal of Operational Research |volume=157 |issue=2 |pages=409–428|doi = 10.1016/S0377-2217(03)00271-6 }}</ref>
and the European subsidies for equalizing unemployment rates among 271 German regions.<ref name="Tangian2008RegionalEnemployment">{{Cite journal|last=Tangian |first=Andranik |year=2008
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