Cardinality Negative (cardn_neg)
Contents
Cardinality Negative. Number of scaled components of -(vector) exceeding some threshold
Syntax
cardn_neg(w, matrix) |
short call |
cardn_neg_name(w, matrix) |
call with optional name |
Parameters
matrix is a PSG matrix:
where the header row contains names of variables (except scenario_benchmark). Other rows contain numerical data, 
. The second numerical row is optional. 
and 
define point for left cardinality “jump” for every variable. If the second numerical row is not present, then, by default, 
. The scenario_benchmark column is optional. If scenario_benchmark column is not present, then, by default, 
. The coefficient z is dummy and it is not used for calculation.
 | is a threshold value. |
defines “jump steepness“.
Mathematical Definition
Cardinality Negative function is calculated as follows
,
where
is small threshold value,
is an argument of Cardinality Negative function.
Remarks
It is recommended to select the multiplier row equal to the unit vector and 
. For instance if decision variables are measured in thousands than 
.
For right side jump use function cardn_pos .
Example
See also
Cardinality Positive, Cardinality, Buyin Positive, Buyin Negative, Buyin, Fixed Charge Positive, Fixed Charge Negative, Fixed Charge