Evaluating Lipschitz Constants for Functions Given by Algorithms

Authors:
João Batista Oliveira
Affiliations:
Faculdade de Informática, Pontifícia Universidade Católica do Rio Grande do Sul, 90619-900 Porto Alegre, Brazil. oliveira@kriti.inf.pucrs.br
Venue:
Computational Optimization and Applications
Year:
2000

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Abstract

This paper describes an efficient method (O(n)) to evaluate the Lipschitz constant for functions described in some algorithmic language. Considering arithmetical operations as the basis of the algorithmic language and supported by control structures, the rules to evaluate such Lipschitz constants are presented and their correctness is proved. An extension of the method to evaluate Lipschitz constants over interval domains is also presented. Examples are presented, but the effectiveness of the method is doubtful when compared to other approaches, and effective enhancements based on slope evaluations are also explored.