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Jonker, P. and Still, G.J. and Twilt, F.
(2009)
On the stratification of a class of specially structured matrices.
Optimization, 58 (6).
pp. 685-712.
ISSN 0233-1934
*** ISI Impact 0,616 ***
Full text available as:
Official URL: http://dx.doi.org/10.1080/02331930701763793  AbstractWe 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.
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