  This paper considers distributed optimization algorithms, with application in
binary classification via distributed support-vector-machines (D-SVM) over
multi-agent networks subject to some link nonlinearities. The agents solve a
consensus-constraint distributed optimization cooperatively via continuous-time
dynamics, while the links are subject to strongly sign-preserving odd nonlinear
conditions. Logarithmic quantization and clipping (saturation) are two examples
of such nonlinearities. In contrast to existing literature that mostly
considers ideal links and perfect information exchange over linear channels, we
show how general sector-bounded models affect the convergence to the optimizer
(i.e., the SVM classifier) over dynamic balanced directed networks. In general,
any odd sector-bounded nonlinear mapping can be applied to our dynamics. The
main challenge is to show that the proposed system dynamics always have one
zero eigenvalue (associated with the consensus) and the other eigenvalues all
have negative real parts. This is done by recalling arguments from matrix
perturbation theory. Then, the solution is shown to converge to the agreement
state under certain conditions. For example, the gradient tracking (GT) step
size is tighter than the linear case by factors related to the upper/lower
sector bounds. To the best of our knowledge, no existing work in distributed
optimization and learning literature considers non-ideal link conditions.
