On the stratification of a class of specially structured matrices

P. Jonker, Peter Jonker, Georg J. Still, F. Twilt, Frank Twilt

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We consider specially structured matrices representing optimization problems with quadratic objective functions and (finitely many) affine linear equality constraints in an n-dimensional Euclidean space. The class of all such matrices will be subdivided into subsets ['strata'], reflecting the features of the underlying optimization problems. From a differential-topological point of view, this subdivision turns out to be very satisfactory: Our strata are smooth manifolds, constituting a so-called Whitney Regular Stratification, and their dimensions can be explicitly determined. We indicate how, due to Thom's Transversality Theory, this setting leads to some fundamental results on smooth one-parameter families of linear-quadratic optimization problems with ( finitely many) equality and inequality constraints.
Original languageUndefined
Article number10.1080/02331930701763793
Pages (from-to)685-712
Number of pages28
JournalOptimization
Volume58
Issue number6
DOIs
Publication statusPublished - 2009

Keywords

  • EWI-17300
  • IR-69759
  • METIS-264494

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