2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66477Using 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.No figures, this version removes typos, improves notation and corrects two minor errors in section 3 and 4Optimization and Control90C22;90C27;90C10text