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A Semidefinite Representation for some Minimum Cardinality Problems

Alexandre d'Aspremont
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Abstract

Using techniques developed in [Lasserre02], we show that some minimum cardinality problems subject to linear inequalities can be represented as finite sequences of semidefinite programs. In particular, we provide a semidefinite representation of the minimum rank problem on positive semidefinite matrices. We also use this technique to cast the problem of finding convex lower bounds on the objective as a semidefinite program.

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Alexandre d'Aspremont. 2003-02-27. A Semidefinite Representation for some Minimum Cardinality Problems. https://arxiv.org/abs/math/0302092

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