Mixed Integer Linear Programming Problem
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I am trying to solve a integer linear programming problem, written in matlab as follows:
fs = 170;
Ts = 1/fs;
t = 0:Ts:1;
fo = 20;
f = -1*ones(1,171);
intcon = 1:length(f); %% All variables are integers.
lb = zeros(length(171),1); %%
ub = 1*ones(length(171),1); %% Enforces the optimization variables are binary.
Aeq = [];
beq = [];
A = ADS; %% Teoplitz Matrix (Convolution to Matrix Multiplication)
b = 5.*sin(2*pi*fo*t); %%
x = intlinprog(f,intcon,A,b,Aeq,beq,lb,ub);
When I try to solve this in matlab using default options, it tells me that no feasible solution exists. Then I removed the integer constraints and tried resolving it using linprog solver. It again tells me the same thing. I do not see any reason why this should happen.
I was just wondering if the reason for this might be the linear constraint b which is a sinusoidal? When I put b as a constant value, it solves the optimization problem.
Can someone please give me a bit more insight as to the reason of infeasibility in this case?
4 Comments
Walter Roberson
on 23 Dec 2020
What are the mininum and maximum number of positive and negative entries in one row of the toeplitz matrix?
For example if all of the entries except for (say) 3 were negative, and the rest positive, then with your f being all negative 1, that could turn into a sum that could not feasibly be negative enough to satisfy the 5*sin() being as low as -5
Answers (2)
Matt J
on 24 Dec 2020
Edited: Matt J
on 24 Dec 2020
Since your unknown x(i) are bounded between 0 and 1, an upper bound on abs(A*x) is sum(abs(A),2). It seems doubtful to me that sum(abs(A),2) for the matrix you've shown could ever exceed 5. Therefore A*x could never reach a value less than -5, which it would have to in order for A*x to be bounded from above by b=5.*sin(2*pi*fo*t).
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Alan Weiss
on 27 Dec 2020
You might find the following documentation useful:
Alan Weiss
MATLAB mathematical toolbox documentation
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