Our method builds a sequence of inner polytopic approximations of a convex set. New vertices of such an approximation are obtained by optimizing linear functions (constructed from the facet-defining inequalities for the inner polytope) over the set. During several decades, it has been reinvented in many different contexts such as concave programming, convex hull computation, computation of Newton polytopes in algebraic geometry, multi-objective optimization and computational molecular biology.
Maxim Demenkov
Maxim Demenkov got his PhD in Automatic Control from De Montfort University (UK). He works now as Engineering Mathematician at the Institute of Control Sciences in Moscow, Russia.