Towards historical roots of necessary conditions of optimality. Regula of Peano

Details Towards historical roots of necessary conditions of optimality. Regula of Peano Towards historical roots of necessary conditions of optimality. Regula of Peano

2010-02-24

arxiv.org/abs/1002.4581v1

Control and Cybernetics 36 (2007) 491-518

Mathematics

History and Overview

28 pages, in honour of Professor Stefan Rolewicz and commemorating the 150th anniversary of the birth of Giuseppe Peano (1858-

Scientific paper

At the end of 19th century Peano discerned vector spaces, differentiability, convex sets, limits of families of sets, tangent cones, and many other concepts, in a modern perfect form. He applied these notions to solve numerous problems. The theorem on necessary conditions of optimality (Regula) is one of these. The formal language of logic that he developed, enabled him to perceive mathematics with great precision and depth. Actually he built mathematics axiomatically based exclusively on logical and set-theoretic primitive terms and properties, which was a revolutionary turning point in the development of mathematics.

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