在多项式型变换下具有不变性的算法

On the Algorithms Invariant to Polynomial-Type Scaling

摘要: 本文讨论根据较一般的目标函数模型(3)建立具有非线性尺度不变性的算法的理论依据。文献[2]研究了F(q)是二次函数的情形,我们可以把它看做是用q的二次函数逼近一般的F(q)。本文研究逼近F(q)的一般问题,对于用高阶多项式逼近和用低阶多项式分段逼近的两种策略,分别导出了计算ρ_K的解析表达式,并建立了相应的算法。

Abstract: This paper discusses the algorithms invariant to nonlinear scaling for more general objective function model(3). The case of algorithms was studied in [2] when F(q) is a quadratic function. Here we study a more general problem - approximation F(q) with high-order polynomial and with piecewise low-order polynomial. The analytic formulas of ρ_K for both cases are derived and the corresponding algorithms are established.