FINITE-DIFFERENCE STOCHASTIC SCHEMES FOR MINIMIZING A STRONGLY QUASICONVEX NON-DIFFERENTIABLE FUNCTION ON ℝ<i><sup>n</sup></i>. THE NURMINSKII METHOD

Source abstract

In this work, stochastic approximation methods based on finite-differences are investigated for the problem of minimizing quasiconvex functions. The main result of this work is the derivation of convergence rate estimates for stochastic finite-difference methods in the case of quasiconvex functions. The obtained results significantly extend the applicability of stochastic finite-difference methods to nonsmooth quasiconvex optimization problems and provide a rigorous justification for their use in black-box settings where the oracle returns only function values.