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Typical convex program is very well posed. (English) Zbl 1082.49030
Summary: In this paper we consider the collection of convex programming problems with inequality and equality constraints, in which every problem of the collection is obtained by linear perturbations of the cost function and right-hand side perturbation of the constraints, while the “core” cost function and the left-hand side constraint functions are kept fixed. The main result shows that the set of the problems which are not well-posed is \(\sigma\)-porous in a certain strong sense. Our results concern both the infinite and finite dimensional case. In the last case the conclusions are significantly sharper.

MSC:
49K40 Sensitivity, stability, well-posedness
90C25 Convex programming
90C31 Sensitivity, stability, parametric optimization
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