  A general nonlinear $1$st-order consensus-based solution for distributed
constrained convex optimization is proposed with network resource allocation
applications. The solution is used to optimize continuously-differentiable
strictly convex cost functions over weakly-connected undirected networks, while
it is anytime feasible and models various nonlinearities to account for
imperfections and constraints on the (physical model of) agents in terms of
limited actuation capabilities, e.g., quantization and saturation. Due to such
inherent nonlinearities, the existing linear solutions considering ideal agent
models may not necessarily converge with guaranteed optimality and anytime
feasibility. Some applications also impose specific nonlinearities, e.g.,
convergence in fixed/finite-time or sign-based robust disturbance-tolerant
dynamics. Our proposed distributed protocol generalizes such nonlinear models.
Putting convex set analysis together with nonsmooth Lyapunov analysis, we prove
convergence, (i) regardless of the particular type of nonlinearity, and (ii)
with weak network-connectivity requirements (uniform-connectivity).
