linear optimization using optimization toolbox and minimize array sum

I had dataset of load for 7 days, 1min time interval and I want to put a threshold value. Now claculate a difference D=(load-Threshold) and this D array should be positive by taking modulus and then a array values 'V' with corresponding to the each load data to minimize the sum of array D all data. How to minimize the sum of all elements of D and find the array values of 'V'.

For example:

a = 30;

b = 150;

D = (b-a).*rand(100,1) + a; % load data

Th=110; % threshold

Diff= abs(D-TH);

Now I want to minimize the sum of "Diff" and find a corresponding vector V(100*1) vector for all values.

[Torsten]

Sorry, but I don't understand the general description of your problem.

Maybe a simple example can help to clarify.

[MUKESH KUMAR]

Just take vector D(100*1) values between 50 to150 and there is one Threshold lets say 90 and I want to find out the positive differnece PD=abs(D-Th); and then minimize the sum of PD and find the values of vector V(100*1), after minimizin the sum of PD.

Thanks

[Torsten]

If you are given D and Th, then PD=abs(D-Th) is given. Then also the sum of PD is given. How do you want to minimize the sum of PD if it is already given ?

[MUKESH KUMAR]

Want vector V, for D+V-Th so the PD should be minimum

Answer 1

[Torsten]

https://math.stackexchange.com/questions/113270/the-median-minimizes-the-sum-of-absolute-deviations-the-l-1-norm

Answer 2

[Bruno Luong]

Diff= abs(D-TH);

Now I want to minimize the sum of "Diff"

Threshold = median(D)

[MUKESH KUMAR]

Th is fix for all values and after calculating the Diff, its all values should be minimized and find Vector V(100*1) such that D+V-Th=0;

[Bruno Luong]

Then

V = Th-D

[Torsten]

Th is known in advance ? Then how can you optimize anything if everything is fixed ?

[MUKESH KUMAR]

Want to find out V such that the sum of difference (D-Th) is minimum .

[Bruno Luong]

Then my trivial solution meets that

V = Th-D

[MUKESH KUMAR]

if we neglect that D+V-Th=0 conditon then how can find V with minimizing Diff??

[Bruno Luong]

Why do you neglect something that you want to achieve????

Wonder if you really know what you want.

[MUKESH KUMAR]

Bcoz that constraint is by my misunderstanding and that is not a case in my original case

Thanks