Originally posted by: GMB7_Wang_Kefeng

a,b is positive real decision variable; c is a blooean decision variable. If I want to
express the meaning as follows:
if c=0 then
a=0 and b=0;
if c!=0 then
a!=0 or b!=0
I know these relationship can be expressed into the logistic constraints. But I want to make it as the
linearized expressions, who can tell me whether these relationship can be described into several linearized expressions?
#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: MSaqib

How about c <= a + b? That seems to capture the if c == 0 then a = 0 and b = 0. Depending on your optimization objective function, it might also hold for the other case.
#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: SystemAdmin

Your modelling approach only captures
(a+b == 0) -> (c==0)

The constraints you want to model is

dvar boolean c;
dvar float+ a;
dvar float+ b;
 
(c==0) -> (a==0 && b == 0);
(c==1) -> (a!=0 || b != 0);

What you could do is use some kind of big-M-modelling

Suppose M is some "big number": Then you have

a <= M*c
b <= M*c
a+b >= c*1/M

i.e., when c==0 you get
a <= 0
b <= 0
a+b >= 0
(i.e. all three variables have to be 0)
For c == 1 you get
a <= M
b <= M
a+b >= 1/M
(i.e. a+b take a slightly positive value)

There might as well be other ways to lineralize the constraints.
Typlically the big-M-terms make the model numerically more difficult to solve ...

Hope this will help

Regards
Norbert
#DecisionOptimization
#OPLusingCPLEXOptimizer