On VU-theory for functions with primal-dual gradient structure

We consider a general class of convex functions having what we call primal- dual gradient structure. It includes finitely determined max-functions and maximum eigenvalue functions as well as other in finitely defined max-funct ions. For a function in this class, we discuss a space decomposition that a llows us to identify a subspace on which the function appears to be smooth. Moreover, using the special structure of such a function, we compute smoot h trajectories along which certain second-order expansions can be obtained. We also give an explicit expression for the Hessian of a related Lagrangia n.