A representation method for PWL functions oriented to parallel processing
Mathematical and Computer Modelling: An International Journal
Linearly constrained global optimization via piecewise-linear approximation
Journal of Computational and Applied Mathematics
Analytical expression of explicit MPC solution via lattice piecewise-affine function
Automatica (Journal of IFAC)
Discrete piecewise linear functions
European Journal of Combinatorics
A special kind of neural networks: continuous piecewise linear functions
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
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Continuous Piecewise-Linear (PWL) functions can be represented by a scheme that selects adequately the linear components of the function without considering explicitly the boundaries. The representation method based on the Lattice Theory, that we call the lattice PWL model, is a form that fits that scheme. In this paper, two domain partitions are proposed that give rise to region configurations practically meaningful for the realizability of lattice models. In one of those partitions, each region is uniquely determined by one of the linear function. The other region configuration is derived from the rearrangement in ascending order of the linear components. Both configurations are discussed and connected with the domain partition generated by the set of boundaries, frequently considered when dealing with PWL functions. The realization method of lattice models is adapted to the three region configurations, comparing the efficiency of the resulting versions.