# define a dummy decision variable for optimization problem

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Nourhan Elsayed on 8 Jul 2020
Commented: Nourhan Elsayed on 9 Jul 2020
Dear All,
i want to define a matrix "Ld" of decision variables whose the size of matix "Ld" is not fixed, it is a function on "m", wheares "m" is ,itself, one of the decision variables and could have any number from 1 : 3. thus, next matrix contains all possible elements of Ld
Ld = [x(1:j) ; x(j+1:2*j); x(2*j+1:3*j); x(3*j+1:4*j); x(4*j+1:5*j);x (5*j+1:6*j)]
Ld_L = Ld(1:m,1:j);
Ld_R = Ld(1+m : 2*m,1:j);
Ld has no any contribution in calculations. only Ld_L and Ld_R are participating on calculations
if m <3 then the rest of elements of Ld are not used
note, their are other decision variables with index starting from X(6*j + 1) but i dont mention them here.
my question is,what is the impact of the other elements of Ld, which are not used on calculation in case m < 3, but they are defined as deciosno variable for the optimization algorithm, since they are part of X matrix,

Alan Weiss on 9 Jul 2020
It sounds to me as if the best approach is to solve three separate optimization problem, one for each value of m, and compare those three solutions.
Alan Weiss
MATLAB mathematical toolbox documentation

#### 1 Comment

Nourhan Elsayed on 9 Jul 2020
Thank you Alan You gave me a good suggestion, i will try it and see.