Abstract:
We derive a new genericity result for nonlinear semidefinite programming (NLSDP). Namely, almost all linear perturbations of a given NLSDP are shown to be nondegenerate. Here, nondegeneracy for NLSDP refers to the transversality constraint qualification, strict complementarity and second-order sufficient condition. A reduced NLSDP is locally considered by transforming equivalently thesemidefinite constraint to a smaller dimension via Schur complement.
While deriving optimality conditions for the reduced NLSDP, the `$H$-term” in the second-order sufficient condition vanishes. This allows us to access the proof of the genericity result for NLSDP.