  In this work, we derive second-order optimality conditions for nonlinear
semidefinite programming (NSDP) problems, by reformulating it as an ordinary
nonlinear programming problem using squared slack variables. We first consider
the correspondence between Karush-Kuhn-Tucker points and regularity conditions
for the general NSDP and its reformulation via slack variables. Then, we obtain
a pair of "no-gap" second-order optimality conditions that are essentially
equivalent to the ones already considered in the literature. We conclude with
the analysis of some computational prospects of the squared slack variables
approach for NSDP.
