赋范空间中逐段仿射不等式系统的误差界

Error Bounds of Piecewise Affine Inequality System in Infinite Dimensional Norm Space

文章通过商空间理论,证明了无穷维赋范空间中逐段仿射不等式系统必定存在局部差界,并给出了逐段仿射不等式系统存在整体误差界的一个充要条件。

We consider the error bounds for a piecewise affine inequality system in infinite dimensional norm space and through the theory of quotient space,we prove that there exist local error bounds for this system. Moreover,we present a necessary snd sufficient condition for this system to have a global error bound.