  Under study is the new class of geometrical extremal problems in which it is
required to achieve the best result in the presence of conflicting goals; e.g.,
given the surface area of a convex body $\mathfrak x$, we try to maximize the
volume of $\mathfrak x$ and minimize the width of $\mathfrak x$ simultaneously.
These problems are addressed along the lines of multiple criteria decision
making.
