Abstract
In this paper, we propose a method for finding the best piecewise linearization of nonlinear functions. For this aim, we try to obtain the best approximation of a nonlinear function as a piecewise linear function. Our method is based on an optimization problem. The optimal solution of this optimization problem is the best piecewise linear approximation of nonlinear function. Finally, we examine our method to some examples.
Highlights
The linearization of nonlinear systems is an efficient tool for finding approximate solutions and treatment analysis of these systems, especially in application [1]-[3]
The optimization problem (9) is a nonlinear programming problem. We reduce this problem to a linear programming problem by relation ri − si =ri + si such that ri ⋅ si =0
Our method for piecewise linearization of nonlinear functions is extensible to R = (−∞, +∞) by the function : (−∞, +∞) → [0,1]
Summary
The linearization of nonlinear systems is an efficient tool for finding approximate solutions and treatment analysis of these systems, especially in application [1]-[3]. In many applications for nonlinear and nonsmooth functions, we are faced to some problems. Piecewise linearization is a more efficient tool for finding approximate solutions. Our aim is to approximate the nonlinear function F by a piecewise linear function as follows:. (2014) The Best Piecewise Linearization of Nonlinear Functions. As we know, this partitioning has bellow properties: 1) ∀i, j = 1, 2, , N; ∩ Ai Aj = ∅, Ai ∈ Rn. χAi ( x) is a characteristic function on such that:. By above definition f ∗ is optimal solution of the following optimization problem: Min F − f (6).
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