2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218951Under 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.Metric GeometryOptimization and Control52A40; 90B50text