  In this paper we look at a class of random optimization problems. We discuss
ways that can help determine typical behavior of their solutions. When the
dimensions of the optimization problems are large such an information often can
be obtained without actually solving the original problems. Moreover, we also
discover that fairly often one can actually determine many quantities of
interest (such as, for example, the typical optimal values of the objective
functions) completely analytically. We present a few general ideas and
emphasize that the range of applications is enormous.
