2013/03/13 by Salvador Gigena, Gigena, Salvador
Computer Science · Earth and Planetary Sciences · Mathematics · #26B10 #26B12 (Primary) #26B99 #54C30 (Secondary) #Advanced Optimization Algorithms Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geophysics and Gravity Measurements #Numerical Methods and Algorithms #math.CA #msc:26B10 #msc:26B12 #msc:26B99 #msc:54C30
paper · pdf · doi:10.48550/arxiv.1303.3184
42 pages, 3 figures
arxiv created 2013/03/13 · openalex publication_date 2013/03/13 · arxiv updated 2013/03/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.