  This work presents a novel version of recently developed Gauss-Newton method
for solving systems of nonlinear equations, based on upper bound of solution
residual and quadratic regularization ideas. We obtained for such method global
convergence bounds and under natural non-degeneracy assumptions we present
local quadratic convergence results. We developed stochastic optimization
algorithms for presented Gauss-Newton method and justified sub-linear and
linear convergence rates for these algorithms using weak growth condition (WGC)
and Polyak-Lojasiewicz (PL) inequality. We show that Gauss-Newton method in
stochastic setting can effectively find solution under WGC and PL condition
matching convergence rate of the deterministic optimization method. The
suggested method unifies most practically used Gauss-Newton method
modifications and can easily interpolate between them providing flexible and
convenient method easily implementable using standard techniques of convex
optimization.
