# Maximal enclosed D-simplex

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?