Direct Methods in the Parametric Moving Boundary Variational Problem

Abstract

In this article, we consider the moving boundary variational problem in a parametric form. By means of the tools of the nonsmooth analysis and exact penalty functions, a new form of necessary conditions for an extremum is obtained. The new conditions make it possible to construct new (“direct”) numerical algorithms. Numerical experiments have demonstrated efficiency of the proposed algorithms and the expediency to further promotion of the approach.

Keywords:

• Calculus of variations
• Exact penalties
• Method of hypodifferential descent
• Nonsmooth analysis
• Subdifferential

Mathematics Subject Classification:

• 49M05
• 49J52

ACKNOWLEDGMENTS

The authors are thankful to the unknown referee for their careful reading the paper and useful remarks.

Part of the special issue, “Variational Analysis and Applications.”