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
S
t
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
S
0
.
To do the computations, iterate
t
from 1 until
nIterations
:
1. Choose a set of indices without replacement where
b
is the batch size.
3. Convergence check:
Stop if
where U is an algorithm-specific vector (argument or gradient) and d is an algorithm-specific power of Lebesgue space.
4. Compute where
T
is an algorithm-specific transformation that updates the function argument.
5. Update
S
t
:
S
t
=
U
(
S
t
-1
), 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
S
.
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
S
.
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.

#### Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804