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In this chapter, we address a problem of calculus of variations: compute the optimal solution of the Plateau problem. We present three different methods illustrated in Fig. 1.2 of Chap. 1 : a direct method via automatic differentiation, an indirect method by solving the optimality conditions and a hybrid method. We finally highlight the non-commutativity of the previous methods which do not necessarily yield the same solution, depending on the choice of discretization.

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Plateau Problem

  • 章节

  • 发表日期：

    2026年

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  • Frédéric Hecht,
  • Gontran Lance,
  • Emmanuel Trélat

摘要

In this chapter, we address a problem of calculus of variations: compute the optimal solution of the Plateau problem. We present three different methods illustrated in Fig. 1.2 of Chap. 1 : a direct method via automatic differentiation, an indirect method by solving the optimality conditions and a hybrid method. We finally highlight the non-commutativity of the previous methods which do not necessarily yield the same solution, depending on the choice of discretization.