Finding an Envelope is an Optimization Problem

The standard approach to finding the envelope of a family of curves or a family of surfaces is shown to be a parameter optimization problem. This statement is first verified by discussing the envelope of a one-parameter family of plane curves. The standard approach is given, and the corresponding op...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 186; no. 2; pp. 453 - 458
Main Author Hull, David G.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2020
Springer Nature B.V
Subjects
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Curves
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Parameters
Theory of Computation
Parameter optimization
Envelopes
Family of curves
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Summary:The standard approach to finding the envelope of a family of curves or a family of surfaces is shown to be a parameter optimization problem. This statement is first verified by discussing the envelope of a one-parameter family of plane curves. The standard approach is given, and the corresponding optimization problem is established. Extensions of the envelope problem to multiple parameters and families of surfaces are considered, as well as envelope problems that cannot be solved by the standard approach, for example, problems involving multiple parameters subject to constraints on the parameters.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-020-01707-9