  The paper deals with a Bolza optimal control problem for a dynamical system
which motion is described by a delay differential equation under an initial
condition defined by a piecewise continuous function. For the value functional
in this problem, the Cauchy problem for the Hamilton-Jacobi-Bellman equation
with coinvariant derivatives is considered. Minimax and viscosity solutions of
this problem are studied. It is proved that both of these solutions exist, are
unique and coincide with the value functional.
