A piecewise linear function is a function composed of some number of linear segments defined over an equal number of intervals, usually of equal size. For example, consider the function y=x^3 over the interval [1,2]. If y(x) is approximated by a piecewis
The Choquet and Sugeno (fuzzy) integrals are examples of piecewise linear functions on a finite dimensional space R[sup n]. In this paper we consider piecewise linear functions as aggregation functions and establish a Max-Min polynomial representation of these functions.Ovchinnikov...
形如\max_{i=1,...,m} (\textbf{c}_i' \textbf{x} + d_i) 的函数被称为 分段线性凸函数 (piecewise linear convex function). 一个简单的例子是 f(x) = |x| = \max\{ x, -x\} , 如图1.2(b)所示, 分段线性凸函数可以被用于近似一般凸函数....
Graph piecewise-defined functions, including step functions and absolute value functions. *(Modeling Standard) Notes, Examples, and Exam Questions Piecewise Function: A function whose rule includes more than one formula. The formula for each piece of the function is applied to certain values of the...
Piecewise linear functions In CP Optimizer, piecewise linear functions are typically used to model a known function of time, such as the cost incurred for completing an activity after a known date t (see Expressions over Interval Variables). A piecewise linear function F(t) is defined by a ...
首先，我们定义了凸函数与凹函数。若函数对于所有参数值，在给定区间内函数值不超过连接两点的直线，则称该函数为凸函数。若函数对于所有参数值，在给定区间内函数值不小于连接两点的直线，则称该函数为凹函数。凸函数和凹函数的图形特征如图1.1所示。值得注意的是，若函数同时为凸且凹，则该函数被称为...
It is a periodic,piecewise linear, continuous real function. WikiMatrix The square of each of these is approximated usingpiecewise linearcircuits. WikiMatrix Important sub-classes ofpiecewise linearfunctions include the continuouspiecewise linearfunctions and the convexpiecewise linearfunctions. ...
Fig. 2.6 A convex piecewise-linear function (solid lines) of a single variable \(x\). The function is defined as the maximum of 3 affine functions. The epigraph \(f(x) \leq t\) (see Sec. 12 (Notation and definitions)) has an equivalent formulation with \(m\) inequalities: \[a_...
Multiple objective piecewise linear programs (MOPLPs) speci cally arise in location problems, where given a number of exisiting facilities a new facility has to be located so that some objectives are optimized. The objectives are often in the form of piecewise linear functions due to the fact ...
Weissenberger, S., "Piecewise-Quadratic and Peice- wise-Linear Lyapunov Functions for Discontinuous Systems," Int. J. Contr., Vol. 10, No. 2, pp. 171-180 (1969).S. Weissenberger, Piecewise-quadratic and piecewise-linear Lyapunov functions for discon- tinuous systems, Internat. J. Control...