# linear optimization using optimization toolbox and minimize array sum

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MUKESH KUMAR on 31 Jul 2019
Commented: MUKESH KUMAR on 31 Jul 2019
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.

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MUKESH KUMAR on 31 Jul 2019
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 on 31 Jul 2019
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 on 31 Jul 2019
Want vector V, for D+V-Th so the PD should be minimum

Torsten on 31 Jul 2019
https://math.stackexchange.com/questions/113270/the-median-minimizes-the-sum-of-absolute-deviations-the-l-1-norm

Bruno Luong on 31 Jul 2019
Edited: Bruno Luong on 31 Jul 2019
Diff= abs(D-TH);
Now I want to minimize the sum of "Diff"
Threshold = median(D)

MUKESH KUMAR on 31 Jul 2019
if we neglect that D+V-Th=0 conditon then how can find V with minimizing Diff??
Bruno Luong on 31 Jul 2019
Why do you neglect something that you want to achieve????
Wonder if you really know what you want.
MUKESH KUMAR on 31 Jul 2019
Bcoz that constraint is by my misunderstanding and that is not a case in my original case
Thanks