Is it possible to construct convex
D-polyhedron $P$ that there exists a
D-simplex $A$ spanned on vertices of $P$, that its volume $V_A$ only decrease if any of its vertices is shifted into a neighbouring vertex of $P$, but there is another
D-simplex $B$ spanned on vertices of $P$ the volume of which $V_B$ is greater then volume of $A$?
Another words can I iteratively find maximal simplex enclosed by convex hull of a set of points or are there local maxima?