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

TL;DR

This paper explores the historical development of Peano's foundational concepts, emphasizing his formal approach and the origins of necessary conditions of optimality in mathematics.

Contribution

It highlights Peano's pioneering axiomatic framework and his formulation of the theorem on necessary conditions of optimality, connecting historical roots to modern mathematical analysis.

Findings

Peano developed a formal logical language for mathematics.

He applied these concepts to solve optimization problems.

His work laid the groundwork for modern necessary conditions in optimality.

Abstract

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.