On the stratification of a class of specially structured matrices

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Jonker, Peter and Still, Georg and Twilt, Frank (2009) On the stratification of a class of specially structured matrices. Optimization, 58 (6). pp. 685-712. ISSN 0233-1934

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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.
Item Type:Article
Copyright:© 2009 Taylor & Francis
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/69759
Official URL:http://dx.doi.org/10.1080/02331930701763793
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