Developer Guide and Reference

  • 2021.2
  • 03/26/2021
  • Public Content
Contents

Sum of Functions

The sum of functions LaTex Math image. is a function that has the form of a sum:
LaTex Math image.
For given set of the indices LaTex Math image., LaTex Math image., LaTex Math image., the value and the gradient of the sum of functions in the argument LaTex Math image. has the format:
LaTex Math image.
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The set of the indices
I
is called a batch of indices.

Computation

Algorithm Input
The sum of functions algorithm accepts the input described below. Pass the
Input ID
as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.
Input ID
Input
argument
A numeric table of size LaTex Math image. with the input argument of the objective function.
Algorithm Parameters
The sum of functions algorithm has the following parameters:
Parameter
Default Value
Description
resultsToCompute
gradient
The 64-bit integer flag that specifies which characteristics of the objective function to compute.
Provide one of the following values to request a single characteristic or use bitwise OR to request a combination of the characteristics:
value
Value of the objective function
nonSmoothTermValue
Value of non-smooth term of the objective function
gradient
Gradient of the smooth term of the objective function
hessian
Hessian of smooth term of the objective function
proximalProjection
Projection of proximal operator for non-smooth term of the objective function
lipschitzConstant
Lipschitz constant of the smooth term of the objective function
gradientOverCertainFeature
Certain component of gradient vector
hessianOverCertainFeature
Certain component of hessian diagonal
proximalProjectionOfCertainFeature
Certain component of proximal projection
Algorithm Output
For the output of the sum of functions algorithm, see Output for objective functions.

Product and Performance Information

1

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