Author： Jonker Peter Still Georg Twilt Frank
Publisher： Taylor & Francis Ltd
ISSN： 0233-1934
Source： Optimization, Vol.58, Iss.6, 2009-08, pp. : 685-712
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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.
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