Constrained Optimization on Hierarchies and Braids of Partitions
L'optimisation contrainte sur des hiérarchies et tresses de partitions
Résumé
This theoretical paper provides a basis for the optimality of scale-sets by Guigues [6] and the optimal pruning of binary partition trees by Salembier-Garrido [11]. They extract constrained-optimal cuts from a hierarchy of partitions. Firstly, this paper extends their results to a larger family of partitions, namely the braid [9]. Secondly, the paper shows the dependence of valid constraint function values and multiplier values in a Lagrangian optimization framework. Lastly, but most importantly, it also proposes the energetic order and energetic lattice based solutions for the constraint optimization problem. This approach operates on a partition based constraint thus ensuring the existence of a valid multiplier and constraint value.
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ConstrainedOptBraids_ISMM2015.pdf (327.67 Ko)
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PosterISMM2015.pdf (642.88 Ko)
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