  Detecting hidden convexity is one of the tools to address nonconvex
minimization problems. After giving a formal definition of hidden convexity, we
introduce the notion of conditional infimum, as it will prove instrumental in
detecting hidden convexity. We develop the theory of the conditional infimum,
and we establish a tower property, relevant for minimization problems. Thus
equipped, we provide a sufficient condition for hidden convexity in nonconvex
minimization problems. We illustrate our result on nonconvex quadratic
minimization problems. We conclude with perspectives for using the conditional
infimum in relation to the so-called S-procedure, to couplings and conjugacies,
and to lower bound convex programs.
