Some Results on Maxima and Minima of Real Functions of Vector Variables: A New Perspective
Bibiano Martin Cerna Maguiña,
Dik Dani Lujerio Garcia,
Victor Pocoy Yauri,
Vladimir Giovanni Rodriguez Sabino,
Ruben Mario Leiva Bernuy
Affiliations
Bibiano Martin Cerna Maguiña
Academic Department of Mathematics, Science Faculty, Santiago Antúnez de Mayolo National University, Shancayan Campus, Av. Centenario 200, Huaraz 02000, Peru
Dik Dani Lujerio Garcia
Academic Department of Mathematics, Science Faculty, Santiago Antúnez de Mayolo National University, Shancayan Campus, Av. Centenario 200, Huaraz 02000, Peru
Victor Pocoy Yauri
Academic Department of Mathematics, Science Faculty, Santiago Antúnez de Mayolo National University, Shancayan Campus, Av. Centenario 200, Huaraz 02000, Peru
Vladimir Giovanni Rodriguez Sabino
Academic Department of Mathematics, Science Faculty, Santiago Antúnez de Mayolo National University, Shancayan Campus, Av. Centenario 200, Huaraz 02000, Peru
Ruben Mario Leiva Bernuy
Academic Department of Mathematics, Science Faculty, Santiago Antúnez de Mayolo National University, Shancayan Campus, Av. Centenario 200, Huaraz 02000, Peru
This article presents a method for proving several theorems that enable the determination of the maxima and minima of certain classes of real-valued functions with vector variables, without relying on the classical theory based on partial derivatives. However, the main objective of this work is not to compare this approach with existing methods but, rather, to extend the study of extrema in real functions of vector variables that are not differentiable, as illustrated in Example 1. Each theorem is accompanied by various examples that demonstrate its applicability. The results are based on Theorems 1 and 2, as well as the selection of an appropriate connection between Theorem 2 and the functions to be optimized. Additionally, definitions related to the hierarchy between variables within a given domain are introduced, providing the theoretical framework necessary for the development of the proposed results.
