stochastic quasigradient methods and their application to system optimization^†

Stochastic quasigradient methods generalize the well-known stochastic approximation methods for uncnstrained optimization of the expectation of a random function to problems involving general constraints for deterministic nonlinear optimization problems.

Abstract

This paper systematically surveys the development of stochastic quasigradient (SQG) methods.These metods make it possible to solve optimization problems without calculating the precise valuesw of objectives and constraints (le alone of their derivatives). For deterministic nonlinear optimization problems, these methods can be regarded as methods of randomsearch. For stochastic programming problems. SQG methods generalize the well-known stochastic approximation methods for uncnstrained optimization of the expectation of a random function to problems involving general constraints.