A semismooth Newton method for tensor eigenvalue complementarity problem

Zhongming Chen, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)

Abstract

ÂIn this paper, we consider the tensor eigenvalue complementarity problem which is closely related to the optimality conditions for polynomial optimization, as well as a class of differential inclusions with nonconvex processes. By introducing an NCP-function, we reformulate the tensor eigenvalue complementarity problem as a system of nonlinear equations. We show that this function is strongly semismooth but not differentiable, in which case the classical smooth methods cannot apply. Furthermore, we propose a damped semismooth Newton method for tensor eigenvalue complementarity problem. A new procedure to evaluate an element of the generalized Jacobian is given, which turns out to be an element of the B-subdifferential under mild assumptions. As a result, the convergence of the damped semismooth Newton method is guaranteed by existing results. The numerical experiments also show that our method is efficient and promising.
Original languageEnglish
Pages (from-to)109-126
Number of pages18
JournalComputational Optimization and Applications
Volume65
Issue number1
DOIs
Publication statusPublished - 1 Sep 2016

Keywords

  • B-subdifferential
  • NCP-function
  • Semismooth Newton method
  • Tensor eigenvalue complementarity problem

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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