Narrowing the difficulty gap for the Celis–Dennis–Tapia problem

Immanuel M. Bomze, Michael L. Overton

Research output: Contribution to journalArticlepeer-review


We study the Celis–Dennis–Tapia (CDT) problem: minimize a non-convex quadratic function over the intersection of two ellipsoids. In contrast to the well-studied trust region problem where the feasible set is just one ellipsoid, the CDT problem is not yet fully understood. Our main objective in this paper is to narrow the difficulty gap that occurs when the Hessian of the Lagrangian is indefinite at all Karush–Kuhn–Tucker points. We prove new sufficient and necessary conditions both for local and global optimality, based on copositivity, giving a complete characterization in the degenerate case.

Original languageEnglish (US)
Pages (from-to)459-476
Number of pages18
JournalMathematical Programming
Issue number2
StatePublished - Jul 27 2015


  • Copositive matrices
  • Global optimality condition
  • Non-convex optimization
  • Polynomial optimization
  • Trust region problem

ASJC Scopus subject areas

  • Software
  • General Mathematics


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