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Prioritized optimization by Nash games : towards an adaptive multi-objective strategy

Abstract : This work is part of the development of a two-phase multi-objective differentiable optimization method. The first phase is classical: it corresponds to the optimization of a set of primary cost functions, subject to nonlinear equality constraints, and it yields at least one known Pareto-optimal solution x A. This study focuses on the second phase, which is introduced to permit to reduce another set of cost functions, considered as secondary, by the determination of a continuum of Nash equilibria, {xε} (ε ≥ 0), in a way such that: firstly, x0 = x A (compatibility), and secondly, for ε sufficiently small, the Pareto-optimality condition of the primary cost functions remains O(ε 2), whereas the secondary cost functions are linearly decreasing functions of ε. The theoretical results are recalled and the method is applied numerically to a SuperSonic Business Jet (SSBJ) sizing problem to optimize the flight performance.
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Contributor : Jean-Antoine Désidéri Connect in order to contact the contributor
Submitted on : Tuesday, November 16, 2021 - 2:28:05 PM
Last modification on : Friday, July 8, 2022 - 10:04:40 AM
Long-term archiving on: : Thursday, February 17, 2022 - 7:42:16 PM


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Jean-Antoine Désidéri, Régis Duvigneau. Prioritized optimization by Nash games : towards an adaptive multi-objective strategy. ESAIM: Proceedings and Surveys, 2021, 71, pp.54-63. ⟨10.1051/proc/202171106⟩. ⟨hal-03430912⟩



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