5 problems

Let $r$ be the rational function defined in the paper, let $P$ be a polytope, let $f(x)=r(x)+I_P(x)$, and let $v$ be a vertex of $P$ satisfying $\xi_1(v)=\xi_2(v)=0$. Vertex conjec…

Measurability-removal conjecture. The $w^*$-scalar measurability assumption on $\partial\varphi(\bar{x},\cdot)$ imposed in Theorem 2 and satisfied in separable Asplund spaces can b…

Separable-reduction extension conjecture. The results of Theorem 2 and Corollary 1 related to separable Asplund spaces $X$ can be extended to arbitrary Asplund spaces by implementi…

Subdifferential condition. For almost every $t\in(0,\infty)$,

Equivalence of metric regularity and strong metric regularity. Under these hypotheses, metric regularity and strong metric regularity of the subdifferential are the same notions.