Tools for parametrization and explicit solution in Alexandrov surface area measures of isoperimetrical problems with arbitrary constraints on mixed volumes in convex geometry. The theory of supremal generators and Choquet boundaries in Dedekind complete vector lattices also known as Kantorovich spaces. General rules of subdifferential calculus for convex operators including explicit formulas for recalculating solutions and values of convex extremal problems under convex change-of-variables as well as the theory of approximate and infinitesimal solutions. Complete description, of relevance to mathematical economics, for the abstract modules over rings which enjoy the principles of linear programming or separation theory. Classification of tangent cones of nonsmooth analysis (Bouligand, Clarke, Hadamard, etc.) in terms of infinitesimals and quantifiers. Combined nonstandard methods which rest on interplay between the Robinsonian infinitesimal and Boolean valued versions.
Main publications:
Kutateladze S. S., Fundamentals of Functional Analysis, Kluwer Academic Publishers, Dordrecht, 1995
Kusraev A. G., Kutateladze S. S., Subdifferentials: Theory and Applications, Kluwer Academic Publishers, Dordrecht, 1995
Kusraev A. G., Kutateladze S. S., Boolean Valued Analysis, Kluwer Academic Publishers, Dordrecht, 1999
Gordon E. I., Kusraev A. G., Kutateladze S. S., Infinitesimal Analysis, Kluwer Academic Publishers, Dordrecht, 2002
