Stochastic Quasigradient Methods

Introduction

Calculation of SQG

Convergence Properties

Nonsmooth Problems

Averaging Operations

General Constraints

References

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,...,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