  We study a generic class of \emph{random optimization problems} (rops) and
their typical behavior. The foundational aspects of the random duality theory
(RDT), associated with rops, were discussed in \cite{StojnicRegRndDlt10}, where
it was shown that one can often infer rops' behavior even without actually
solving them. Moreover, \cite{StojnicRegRndDlt10} uncovered that various
quantities relevant to rops (including, for example, their typical objective
values) can be determined (in a large dimensional context) even completely
analytically. The key observation was that the \emph{strong deterministic
duality} implies the, so-called, \emph{strong random duality} and therefore the
full exactness of the analytical RDT characterizations. Here, we attack
precisely those scenarios where the strong deterministic duality is not
necessarily present and connect them to the recent progress made in studying
bilinearly indexed (bli) random processes in
\cite{Stojnicnflgscompyx23,Stojnicsflgscompyx23}. In particular, utilizing a
fully lifted (fl) interpolating comparison mechanism introduced in
\cite{Stojnicnflgscompyx23}, we establish corresponding \emph{fully lifted} RDT
(fl RDT). We then rely on a stationarized fl interpolation realization
introduced in \cite{Stojnicsflgscompyx23} to obtain complete
\emph{statitionarized} fl RDT (sfl RDT). A few well known problems are then
discussed as illustrations of a wide range of practical applications implied by
the generality of the considered rops.
