Abstract
We consider families of optimization problems with quadratic object function and affine linear constraints, which depend smoothly on one real parameter. For a generic subclass of such problems only three different types of (generalized) critical points occur, whereas in the general case (of nonlinear one-parameter families of constrained optimization problems on R n) five types are to be distinguished. We clarify the theoretical background of these phenomena and illustrate the underlying mechanism with simple examples.
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Jonker, P., Still, G. & Twilt, F. One-Parametric Linear-Quadratic Optimization Problems. Annals of Operations Research 101, 221–253 (2001). https://doi.org/10.1023/A:1010980727655
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DOI: https://doi.org/10.1023/A:1010980727655