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