How can I do this L1 integral minimization?
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Greetings,
I have the following integral
where kdx = [pi/16, pi/2], and
I want to minimize the integral above and solving corresponding a_j. But I have no clue how do to it. Can anyone give me some hint?
Thanks.
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답변 (2개)
Bruno Luong
2018년 10월 29일
편집: Bruno Luong
2018년 10월 29일
The problem of linear L1 fit (your case); meaning
argmin_x | M*x - y |_l1
argmin sum abs(M*x - y)
can be reformulated and solved by linear programming (opt toolbox required) using slack variables trick as following
n = length(y);
Aeq = [M speye(n) -speye(n)];
Aeqpr=nonzeros(Aeq);
beq = y(:);
c = [zeros(1,size(M,2)) ones(1,2*n)];
LB = [-inf(1,size(M,2)) zeros(1,2*n)];
UB = [];
c = c(:);
LB = LB(:);
UB = UB(:);
x0 = zeros(size(c)); % guess vector
[sol, f, exitflag] = linprog(c,[],[], Aeq, beq, LB, UB, x0);
x = sol(1:size(M,2));
You just need to build M with sin(k*j*dx) and log(dx).
댓글 수: 8
Bruno Luong
2018년 10월 30일
편집: Bruno Luong
2018년 10월 30일
I don't know how to type a curly "l" (lowercase L), which is the right notation.
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