## Developer Guide and Reference

• 2021.6
• 04/11/2022
• Public Content
Contents

# 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 from until :
1. Choose a set of indices without replacement , , , where is the batch size.
2. Compute the gradient where 3. Convergence check:
Stop if where is an algorithm-specific vector (argument or gradient) and d is an algorithm-specific power of Lebesgue space
4. Compute using the algorithm-specific transformation that updates the function’s argument: 5. Update where 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.
You can resume the computations to get a more precise estimate of the objective function minimum. To do this, pass to the algorithm the results 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

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.