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General Constructive Representations for Continuous Piecewise-Linear Functions.
- Source :
-
IEEE Transactions on Circuits & Systems. Part I: Regular Papers . Sep2004, Vol. 51 Issue 9, p1889-1896. 8p. - Publication Year :
- 2004
-
Abstract
- The problem of constructing a canonical representation for an arbitrary continuous piecewise-linear (PWL) function in any dimension is considered in this paper. We solve the problem based on a general lattice PWL representation, which can be determined for a given continuous PWL function using existing methods. We first transform the lattice PWL representation into the difference of two convex functions, then propose a constructive procedure to rewrite the latter as a canonical representation that consists of at most η-level nestings of absolute-value functions in n dimensions, hence give a thorough solution to the problem mentioned above. In addition, we point out that there exist notable differences between a lattice representation and the two novel general constructive representations proposed in this paper, and explain that these differences make all the three representations be of their particular interests. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15498328
- Volume :
- 51
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Circuits & Systems. Part I: Regular Papers
- Publication Type :
- Periodical
- Accession number :
- 18055488
- Full Text :
- https://doi.org/10.1109/TCSI.2004.834521