[For the entire collection see Zbl 0658.00020.]
The main purpose of the stochastic quasigradient (SQG) methods is the solution of optimization problems with a complex nature of objective functions and constraints. For the stochastic programming problems, SQG methods generalize the well-known stochastic approximation methods for unconstrained optimization of the expectation of a random function to problems involving general constraints and nondifferentiable functions. For deterministic nonlinear programming problems SQG methods can be regarded as methods of random search.
The purpose of this chapter is a discussion of the main direction in the development of SQG procedures, their applications and an overview of ideas involved in the proofs. The contents of this chapter is close to that of the author’s work in Stochastic 9, 1-36 (1983; Zbl 0512.90079).