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Characterizations of the Strong Basic Constraint Qualifications
Mathematics of Operations Research, 2005In this paper, we characterize the general difference between strong basic constraint qualification (BCQ) and BCQ. For this purpose, we introduce a new measurement, the extent of a subdifferential, and show that for an inequality defined by a proper convex function f, the strong BCQ at a boundary point x of the solution set is equivalent to the ...
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Optimization problems with cardinality constraints are problems with inequality and equality constraints where additionally the number of nonzero components of the solution is bounded. These problems can equivalently be formulated as mixed-integer optimization problems.
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