论文标题
Fitzpatrick和凸功能的奇异性
Singularities of Fitzpatrick and convex functions
论文作者
论文摘要
在带有标量产品$ s（\ cdot，\ cdot）$的伪欧国人空间中，我们表明，$ s $ - 单酮套件上的预测奇异性以及相关的fitzpatrick函数涵盖了可数$ c-c $ surfaces与$ s $ s $ propoduct的正常载体的可数$ c-c $表面。作者：Zaj \'ıček[24]，凸函数$ f $的奇异性可以由$ c-c $表面的可数集涵盖。我们表明，这些表面的普通向量仅限于$ f-f $生成的锥体，其中$ f：= \ text {cl range} \ nabla f $，$ f $的梯度范围的关闭。
In a pseudo-Euclidean space with scalar product $S(\cdot, \cdot)$, we show that the singularities of projections on $S$-monotone sets and of the associated Fitzpatrick functions are covered by countable $c-c$ surfaces having positive normal vectors with respect to the $S$-product. By Zaj\'ıček [24], the singularities of a convex function $f$ can be covered by a countable collection of $c-c$ surfaces. We show that the normal vectors to these surfaces are restricted to the cone generated by $F-F$, where $F:=\text{cl range } \nabla f$, the closure of the range of the gradient of $f$.
