Efficient piecewise-linear function approximation using the uniform metric

1994 ◽  
Author(s):  
Michael T. Goodrich
Keyword(s):  
Linear Function ◽  
Function Approximation ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Linear Function Approximation

scholarly journals Optimal Piecewise Linear Function Approximation for GPU-Based Applications

2016 ◽  
Vol 46 (11) ◽  
pp. 2584-2595 ◽  
Author(s):  
Daniel Berjon ◽  
Guillermo Gallego ◽  
Carlos Cuevas ◽  
Francisco Moran ◽  
Narciso Garcia
Keyword(s):  
Linear Function ◽  
Function Approximation ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Linear Function Approximation

scholarly journals Models and Algorithms for Optimal Piecewise-Linear Function Approximation

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Eduardo Camponogara ◽  
Luiz Fernando Nazari
Keyword(s):  
Function Approximation ◽  
Linear Models ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Linear Functions ◽  
Piecewise Linear Functions ◽  
Linear Function Approximation ◽  
Data Points ◽  
Stochastic Functions ◽  
Piecewise Linear Models

Piecewise-linear functions can approximate nonlinear and unknown functions for which only sample points are available. This paper presents a range of piecewise-linear models and algorithms to aid engineers to find an approximation that fits best their applications. The models include piecewise-linear functions with a fixed and maximum number of linear segments, lower and upper envelopes, strategies to ensure continuity, and a generalization of these models for stochastic functions whose data points are random variables. Derived from recursive formulations, the algorithms are applied to the approximation of the production function of gas-lifted oil wells.

scholarly journals MINLP formulations for continuous piecewise linear function fitting

2021 ◽  
Author(s):  
Noam Goldberg ◽  
Steffen Rebennack ◽  
Youngdae Kim ◽  
Vitaliy Krasko ◽  
Sven Leyffer
Keyword(s):  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Mixed Integer ◽  
Function Fitting ◽  
Computational Performance ◽  
Integer Nonlinear Programming ◽  
Minlp Model ◽  
Necessary Constraints ◽  
Continuous Piecewise Linear Function

AbstractWe consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. 10.1007/s10589-014-9647-y) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.

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