How to maximize system of linear equations?
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Clarisha Nijman
on 26 Nov 2018
Commented: Clarisha Nijman
on 1 Dec 2018
Hello,
Given:
A=[4 3; -1 7; 5 9; 2 4];
x=[x1;x2];
b=[b1; b2; b3; b4];
How can I maximize the linear system of equations: Ax=b?
4 Comments
Matt J
on 26 Nov 2018
Edited: Matt J
on 26 Nov 2018
associated with the maximum possible value of b1, b2, b3 and b4
So the idea is to make all b1..b4 as large as possible? Then clearly x=0 and y=Inf are optimal in the example you've shown. They result in b1=b2=b3=b4=Inf.
More generally, though, you cannot simultaneously maximize the right hand side elements b, because they co-depend on the same variables.
Accepted Answer
Matt J
on 26 Nov 2018
Edited: Matt J
on 27 Nov 2018
6 Comments
Matt J
on 30 Nov 2018
Edited: Matt J
on 30 Nov 2018
Runs fine for me. Here is my complete implementation.
C=[ 0.0038 0.0038 0.0038 0.0038
0.0037 0.0037 0.0037 0.0037
0.0036 0.0036 0.0036 0.0036
0.0034 0.0034 0.0035 0.0035
0.0033 0.0033 0.0034 0.0034
0.0032 0.0032 0.0033 0.0033
0.0031 0.0031 0.0032 0.0033
0.0029 0.0029 0.0031 0.0031
0.0028 0.0028 0.0029 0.0028
0.0027 0.0027 0.0024 0.0023];
A1=C(:,2:end);
A2=-C(:,2:end);
Aleq=[A1;A2];
%The less equal RHS
bleq=[C(:,1) -C(:,1)];
Aeq=ones(3,1);
beq=1;
lb=zeros(3,1);
ub=[];
%initial guess
x0=0.1*rand(3,1);
%Defining the objective function
Cs=C(:,2:4);
[OptArgum, optimalVal] = fminimax(@(x) Cs*x,x0,Aleq,bleq(:),Aeq.',beq,lb,ub);
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