Abstract. We consider the continuous stochastic optimization procedure with semi-Markov switching in the diffusion approximation scheme with the balance condition imposed on singular perturbation of the regression function. The sufficient convergence conditions are established for the regression function, which depends on the uniform ergodic semi-Markov process, by using the properties of extended compensating operator of the Markov renewal of the procedure and its asymptotic representation of perturbed Lyapunov function.

Keywords: stochastic optimization, semi-Markov process compensating operator.