The Farkas Lemma Revisited

The Farkas Lemma is extended to simultaneous linear operator and polyhedral sublinear operator inequalities by Boolean valued analysis. Citation Sobolev Institute of Mathematics, Novosibirsk, 630090 Russia Article Download View The Farkas Lemma Revisited

Dido’s Problem and Pareto Optimality

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 … Read more