A Semidefinite Representation for some Minimum Cardinality Problems

Details A Semidefinite Representation for some Minimum Cardinality Problems A Semidefinite Representation for some Minimum Cardinality Problems

2003-02-09

arxiv.org/abs/math/0302092v2

Mathematics

Optimization and Control

No figures, this version removes typos, improves notation and corrects two minor errors in section 3 and 4

Scientific paper

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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