Background

Problem. Finding of a probability distribution which is the most close to some "prior" probability distribution subject to available information about the distribution

Simplified Problem Statement

Mathematical Problem Statement

Problem dimension and solving time

Solution in Run-File Environment

Solution in MATLAB Environment

 

Background

 

Relative Entropy is used to find a probability distribution which is the most close to some "prior" probability distribution subject to available information about the distribution. For instance, moments of a distribution can be known and we want to find the "best" distribution accounting for this information.

The problem selects 100,000 probability atoms of a discrete probability distribution (100,000 decision variables).

 

Problem

 

Simplified Problem Statement

 

Minimize Entropyr (minimizing Relative Entropy)

 subject to

Linear = 0 (constraint on sum of decision variables (probabilities))

A * x = b (linear equality constraint)

Box constraints (non-negative lower bound for probabilities)

 

where

 

Entropyr = Relative Entropy

A = matrix in the linear equality constraint

b = vector in the right hand side of the linear equality constraint

Box constraints = constraints on individual decision variables

 

Mathematical Problem Statement

 

 

Problem dimension and solving time

 

 

Solution in Run-File Environment

 

 

Input Files to run CS:

 

Output Files:

 

Solution in MATLAB Environment

 

Solved with PSG MATLAB subroutine riskprog (General (Text) Format of PSG in MATLAB):

 

 

Input Files to run CS: