Classifying extrema using intervals

2006/09/14 by M. Gutowski, Gutowski, Marek W.
Computer Science · #Computational Complexity (cs.CC) #F.2.2 #FOS: Computer and information sciences #FOS: Mathematics #Fuzzy Logic and Control Systems #G.1.0 #G.1.2 #J.2 #Mathematical Software (cs.MS) #Neural Networks and Applications #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.cs/0609082

openalex publication_date 2006/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

We present a straightforward and verified method of deciding whether the n-dimensional point x (n>=1), such that ∇ f(x)=0, is the local minimizer, maximizer or just a saddle point of a real-valued function f. The method scales linearly with dimensionality of the problem and never produces false results.

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