Constrained Optimization on Hierarchies and Braids of Partitions
International audience 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...
Main Authors: | , |
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Other Authors: | , , , , , , |
Format: | Conference Object |
Language: | English |
Published: |
HAL CCSD
2015
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Subjects: | |
Online Access: | https://hal.science/hal-01134115 https://hal.science/hal-01134115/document https://hal.science/hal-01134115/file/ConstrainedOptBraids_ISMM2015.pdf |
Summary: | International audience 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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