Intel® oneAPI Data Analytics Library Developer Guide and Reference
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Iterative Solver
The iterative solver provides an iterative method to minimize an objective function that can be represented as a sum of functions in composite form
where:
,
, where
is a convex, continuously differentiable
(smooth) functions, 
is a convex, non-differentiable (non-smooth) function
The Algorithmic Framework of an Iterative Solver
All solvers presented in the library follow a common algorithmic framework. Let
be a set of intrinsic parameters of the iterative solver for updating the argument of the objective function. This set is the algorithm-specific and can be empty. The solver determines the choice of
.
To do the computations, iterate t from 1 until
:
Choose a set of indices without replacement
,
,
, where b is the batch size.Compute the gradient
where 
Convergence check:
Stop if
where U is an algorithm-specific vector (argument or gradient) and d is an algorithm-specific power of Lebesgue spaceCompute
using the algorithm-specific transformation T that updates the function’s argument:
Update
where U is an algorithm-specific update of the set of intrinsic parameters.
The result of the solver is the argument
and a set of parameters
after the exit from the loop.
and
of the previous run of the optimization solver. By default, the solver does not return the set of intrinsic parameters. If you need it, set the optionalResultRequired flag for the algorithm.
Iterative solvers