Version 1
: Received: 8 December 2023 / Approved: 8 December 2023 / Online: 8 December 2023 (09:17:23 CET)
How to cite:
Bosi, G.; Roberto, D.; Zuanon, M. Multi-Objective Optimization by Means of Pairs of Functions. Preprints2023, 2023120596. https://doi.org/10.20944/preprints202312.0596.v1
Bosi, G.; Roberto, D.; Zuanon, M. Multi-Objective Optimization by Means of Pairs of Functions. Preprints 2023, 2023120596. https://doi.org/10.20944/preprints202312.0596.v1
Bosi, G.; Roberto, D.; Zuanon, M. Multi-Objective Optimization by Means of Pairs of Functions. Preprints2023, 2023120596. https://doi.org/10.20944/preprints202312.0596.v1
APA Style
Bosi, G., Roberto, D., & Zuanon, M. (2023). Multi-Objective Optimization by Means of Pairs of Functions. Preprints. https://doi.org/10.20944/preprints202312.0596.v1
Chicago/Turabian Style
Bosi, G., Daris Roberto and Magalì Zuanon. 2023 "Multi-Objective Optimization by Means of Pairs of Functions" Preprints. https://doi.org/10.20944/preprints202312.0596.v1
Abstract
We introduce and discuss a generalization of the classical multi-objective optimization to pairs of functions. This procedure is referred to as bi-multi-objective optimization. A justification of this general optimization procedure is presented, related both to multi-objective optimization under ambiguity concerning individual preferences and to Pareto optimality for a family of preferences with nontransitive indifference. Incidentally, the binary relation naturally associated to a bi-multi-objective optimization problem is represented by a finite bi-multi-utility, which generalizes to the nontransitive case the classical finite multi-utility representation. An important application is presented to Markowitz portfolio selection under ambiguity concerning both the vector of returns and the covariance matrix.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
