Stochastic quasigradient methods. (English) Zbl 0666.90072
Numerical techniques for stochastic optimization, Springer Ser. Comput. Math. 10, 141-185 (1988).
[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).
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).
MSC:
90C30 | Nonlinear programming |
65K05 | Numerical mathematical programming methods |
90C15 | Stochastic programming |
90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |