  Gauge invariant Lagrangian descriptions of irreducible and reducible
half-integer higher-spin mixed-symmetric massless and massive representations
of the Poincare group with off-shell algebraic constraints are constructed
within a metric-like formulation in a $d$-dimensional flat space-time on the
basis of a suggested constrained BRST approach. A Lorentz-invariant resolution
of the BRST complex within the constrained BRST formulations produces a
gauge-invariant Fang-Fronsdal Lagrangian entirely in terms of the initial
triple gamma-traceless spin-tensor field $\Psi_{(\mu)_{n}}$ with
gamma-traceless gauge parameter. The triplet and quartet formulations are
derived. The minimal (un)constrained BRST--BV actions for above formulations
are obtained, from proposed constrained BRST--BV approach to be by appropriate
tools to construct interacting constrained Lagrangians.
