Notations

 

I+1 = the number of columns in the data matrix; i={0,1,...,I} index of columns;

J = the number of rows in the data matrix; j={1,...,J} index of rows;

= vector of decision variables;

= random scenario vector with I+1 columns. This random vector has j=1,...,J ,

 scenarios with equal probabilities 1/J . Every scenario corresponds to j-th

 row of the data matrix;

residual corresponding to row j,  j={1,...,J};

= partial moment two function;

= 0 = threshold value for the partial moment two function;
 

U= upper bound on variable , i={1,...,I};

L= lower bound on variable , i={1,...,I};

 

The case study considers the following optimization problem:

 

 

Optimization Problem 1

 

minimizing partial moment two penalty function

 

                               (CS.1)

 

bounds on variables

 

                               (CS.2)