Inexact quantized quasi-subgradient method for quasi-convex optimization problems

Motivated by applications in distributed optimization, in this paper, we consider the nondifferentiable quantized quasi-convex constrained optimization problem and propose a quantized approximate quasisubgradient method (QAQSGM).Each iteration of the QAQSGM consists of an inexact subgradient iteration and a quantization operator successively.The inexactness stems from computation errors and noise, which come from practical considerations and applications.Assuming that the computational errors and noise are deterministic and bounded, we investigate the convergence analysis and study the effect of the inexactness on the QAQSGM when the constraint set is compact or the objective function has a set of generalized weak sharp minima.