Integer programing for minimization
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- How to solve the following integer optimization problem :
Find B and D such that B,D = Min |Y- XDB|||
where the matrices X,Y are given.
The matrix D must be a diagonal matrix where its diagonal elements are 0 or 1.
2 Comments
Torsten
on 25 May 2016
Which norm do you use ?
Is it correct that the same B appears on both sides of the equation
B = Min |Y- XDB|
?
Best wishes
Torsten.
Answers (1)
Nihar Deodhar
on 23 Jun 2016
Your problem could be solved using fmincon. See Matlab documentation on fmincon for more info.
Set up the objective function as
J = abs(Y- X*D*B);
where I guess X is a known matrix/vector.
Set up B using b1,b2,b3.... etc. the number of variables needed would depend on size of B. choose n number of elements d1,d2,....dn for the square matrix D based on its size.
for instance if B is 3x3, set up b1, b2, ......b9 and if D is 3x3 as well (which would have to be given the size of B) choose d1, d2 and d3 as optimization variables ad set the off diagonal elements in D = 0. So the problem will involve (9+3 = 12) optimization variables in this case. Now you said that diagonal of D should be populated by 1 or 0. Set this range for the parameter bounds in fmincon. It is possible that you might get fractions between 0 and 1 as the optimum, just round it up to either 0 or 1 in the end.
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