Monotonicity and stability of optimal solutions of a minimization problem

Yichen Liu, Behrouz Emamizadeh

Research output: Journal PublicationArticlepeer-review

1 Citation (Scopus)


This paper is concerned with a minimization problem modeling the minimum displacement of an isotropic elastic membrane subject to a vertical force such as a load distribution. In addition to proving existence and uniqueness of optimal solutions, we show that these solutions are monotone and stable, in a certain sense. The main mathematical tool used in the analysis is the tangent cones from convex analysis, which helps to derive the optimality condition. Our results are compatible with physical expectations.

Original languageEnglish
Pages (from-to)94-101
Number of pages8
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number1-3
Publication statusPublished - 1 Aug 2015
Externally publishedYes


  • Displacement
  • Existence
  • Membrane
  • Monotonicity
  • Optimal solutions
  • Optimality conditions
  • Optimization
  • Stability
  • Tangent cones
  • Uniqueness

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics


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