Finding an Envelope is an Optimization Problem

• Published in: Journal of optimization theory and applications Vol. 186; no. 2; pp. 453 - 458
• Main Author: Hull, David G.
• Format: Journal Article
• Language: English
• 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

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...