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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 F0(x) to be minimized (or maximized) and to verify constraints
(1)
for each decision vector x = (x1,...,xn)∈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) Fix of the functions Fi,i = 0,1,...,m are easily calculated. Stochastic