  In this work we are interested in nonlinear symmetric cone problems (NSCPs),
which contain as special cases nonlinear semidefinite programming, nonlinear
second order cone programming and the classical nonlinear programming problems.
We explore the possibility of reformulating NSCPs as common nonlinear programs
(NLPs), with the aid of squared slack variables. Through this connection, we
show how to obtain second order optimality conditions for NSCPs in an easy
manner, thus bypassing a number of difficulties associated to the usual
variational analytical approach. We then discuss several aspects of this
connection. In particular, we show a "sharp" criterion for membership in a
symmetric cone that also encodes rank information. Also, we discuss the
possibility of importing convergence results from nonlinear programming to
NSCPs, which we illustrate by discussing a simple augmented Lagrangian method
for nonlinear symmetric cones. We show that, employing the slack variable
approach, we can use the results for NLPs to prove convergence results, thus
extending a special case (i.e., the case with strict complementarity) of an
earlier result by Sun, Sun and Zhang for nonlinear semidefinite programs.
