格分片线性函数的辨识和优化

Identification and optimization of lattice piecewise-linear functions

格分片线性模型由一个实数矩阵和一个 0 - 1矩阵所确定 ,能够表示任意维变量的全体连续分片线性函数 ,其实数矩阵完全由它的局部线性函数的参数向量所组成。这些特点为辨识分片线性函数和利用线性模型的分析方法解决分片线性模型描述的非线性问题提供了极大的便利。该文引入格分片线性模型解决非线性函数的辨识问题。给出了辨识格分片线性函数的实用算法。并对线性约束下的格分片线性函数优化问题提出了通过线性规划算法确定全局最优解的简单方法。这些工作表明 。

A lattice piecewise linear model is parameterized by a real matrix containing the parametric vectors of all local linear functions and a zero one matrix determining how to connect them, which can represent all continuous piecewise linear functions of any dimension. Practical algorithms are proposed to identify a lattice piecewise linear function from the sampled data and to optimize such an objective function with linear constraints using linear programming. A global optimal solution is guaranteed for the nonlinear optimization problem. It is shown by these works that the lattice piecewise linear model is a powerful tool to solve nonlinear problems.