Cardinality Positive (cardn_pos)
Contents
Cardinality Positive. Number of scaled components of a vector exceeding some threshold
Syntax
cardn_pos(w, matrix) |
short call |
cardn_pos_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 Positive function is calculated as follows
,
where
is small threshold value,
is an argument of Cardinality Positive function.
Remarks
It is recommended to select the multiplier (the first numerical) row equal to the unit vector and 
. For instance if decision variables are measured in thousands than 
.
For left side jump use function carnd_neg.
Example
Case Studies with Cardinality Positive
See also
Cardinality Negative (cardn_neg), Cardinality (cardn), Buyin Positive (buyin_pos), Buyin Negative (buyin_neg), Buyin (buyin), Fixed Charge Positive (fxchg_pos), Fixed Charge Negative (fxchg_neg), Fixed Charge (fxchg).