Constrained local extrema without Lagrange multipliers and the higher derivative test

Publication date: 13 March 2013

Abstract: Two are the main objectives of this article: first, we introduce a method for determining and analyzing constrained local extrema that provides a different alternative to all previous works on the topic, by eliminating Lagrange multipliers and reducing constrained problems to unconstrained ones; Second, we also develop another method for analyzing and determining the nature of known critical points by resorting, when needed, to higher order derivatives. The result presented here constitutes our proposal of solution to a long standing problem: that of extending to higher dimensions what has been known for many years in the case of functions defined on open sets of the real line, regarding the classification of critical points when enough derivatives are also known at those points.

Mathematics Subject Classification ID

Implicit function theorems, Jacobians, transformations with several variables (26B10) Calculus of vector functions (26B12) Real-valued functions in general topology (54C30) Functions of several variables (26B99)

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