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Stochastic Quasigradient Methods

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# Stochastic Quasigradient Methods

### Article Outline

Keywords and Phrases

Introduction

Calculation of SQG

Convergence Properties

Nonsmooth Problems

Averaging Operations

General Constraints

References

Keywords and Phrases Stochastic quasigradient (SQG) methods - Stochastic quasigradients (SQG) - Nonstationary optimization - Generalized differentiable (GD) function - Stochastic approximation - Global optimization

## Introduction

Traditional deterministic optimization methods are used for well defined objective and constraint functions, i. e., when it is possible to calculate exactly

for each decision vector

*F*_{0}(*x*) to be minimized (or maximized) and to verify constraints(1) |

*x*= (*x*_{1},...,*x*_{n})∈*X*, where the set*X*has a "simple" structure (for example, defined by linear constraints). Usually it is also assumed that gradients or subgradients (for nonsmooth functions)*F*_{ix}of the functions*F*_{i},*i*= 0,1,...,*m*are easily calculated.*Stochastic*