Distributed Finite-Sum Constrained Optimization subject to Nonlinearity on the Node Dynamics

The paper correctly states feasibility/sum-invariance for odd nonlinearities with bidirectional links and identifies exact convergence under sector-bounded nonlinearities and only practical convergence under uniform quantization. However, it asserts that the residual F is non-increasing for any sign-preserving nonlinearity without explicitly requiring oddness or a stepsize restriction; this is false in discrete time (a simple 2-node counterexample shows F can increase). The model’s solution pinpoints the missing oddness and stepsize conditions, provides a rigorous vector/incidence formulation, and derives a conservative but sound linear-rate bound under sector conditions, plus an O(δ) neighborhood result for uniform quantization, aligning with the paper’s goals while fixing its gaps. Key statements referenced: update laws and feasibility conditions (9–12, odd implies feasibility), the sign-preserving residual claim and sector-rate formula (13), and the qualitative uniform-quantizer conclusion.