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