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Gauge invariant Lagrangian descriptions of irreducible and reduciblehalf-integer higher-spin mixed-symmetric massless and massive representationsof the Poincare group with off-shell algebraic constraints are constructedwithin a metric-like formulation in a $d$-dimensional flat space-time on thebasis of a suggested constrained BRST approach. A Lorentz-invariant resolutionof the BRST complex within the constrained BRST formulations produces agauge-invariant Fang-Fronsdal Lagrangian entirely in terms of the initialtriple gamma-traceless spin-tensor field $\Psi_{(\mu)_{n}}$ withgamma-traceless gauge parameter. The triplet and quartet formulations arederived. The minimal (un)constrained BRST--BV actions for above formulationsare obtained, from proposed constrained BRST--BV approach to be by appropriatetools to construct interacting constrained Lagrangians.

Constrained BRST-BFV and BRST-BV Lagrangians for half-integer HS fields on $R^{1,d-1}$