Visible to Intel only — GUID: GUID-BC431E52-03DC-4FEF-AAD7-5456BA812A6F
Visible to Intel only — GUID: GUID-BC431E52-03DC-4FEF-AAD7-5456BA812A6F
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 space
Compute 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.
Iterative solvers