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.International Journal of ...
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...
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 ...
Summary: We study the problem of approximating a function $F \\,:\\, \\Bbb R ightarrow \\Bbb R$ by a piecewise-linear function $\\overline{F}$ when the values of $F$ at $\\{x_{1}, \\dots, x_{n}\\}$ are given by a discrete probability distribution. Thus, for each $x_...
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 datet(seeExpressions over Interval Variables). Apiecewise linear functionF(t)is defined by a tupleF = piecewise(S, T, t0, v...