  In various applications, the effect of errors in gradient-based iterations is
of particular importance when seeking saddle points of the Lagrangian function
associated with constrained convex optimization problems. Of particular
interest here are problems arising in power control applications, where network
utility is maximized subject to minimum signal-to-interference-plus-noise ratio
(SINR) constraints, maximum interference constraints, maximum received power
constraints, or simultaneous minimum and maximum SINR constraints. Especially
when the gradient iterations are executed in a disributed fashion, imperfect
exchanges among the link nodes may result in erroneous gradient vectors. In
order to assess and cope with such errors, two running averages (ergodic
sequences) are formed from the iterates generated by the perturbed saddle point
method, each with complementary strengths. Under the assumptions of problem
convexity and error boundedness, bounds on the constraint violation and the
suboptimality per iteration index are derived. The two types of running
averages are tested on a spectrum sharing problem with minimum and maximum SINR
constraints, as well as maximum interference constraints.
