fmincon nonlinear inequality constraint

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hey yo
hey yo 2022-8-9
评论： hey yo 2022-8-9
Hello,
I do a maximum likelihood estimation using fmincon. My code requires doing a Choleski decomposition to the matrix: A=[betas(7) betas(9); betas(9) betas(8)]. Choleski decomposition requires the matrix A to be positive definite. Because A is a 2x2 matrix, positive definiteness require two conditions:
  1. beta(7)>0
  2. beta(7)*beta(8)-beta(9)^2>0
I set the lowerbound of beta(7) to be 0. To satisfy the second nonlinear inequality constraint, I wrote a function
function [c,ceq]=mycons(betas)
ceq=[];
c=-(betas(7)*betas(8)-betas(9)^2);
end
Then I run my fmincon function
[b_out,fval] =fmincon(@(betas)mainlf3(betas,numobs, p),betas,[],[],[],[], lb, ub,@(betas)mycons(betas), options1);
However, the code does not satisfy the nonlinear constraint. It gives me the error:
Error using chol
Matrix must be positive definite.
Can anyone see what I'm doing wrong? Thank you.

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采纳的回答

Matt J
Matt J 2022-8-9
编辑：Matt J 2022-8-9
The nonlinear constraints are not obeyed at all iterations. At iterations where they are not obeyed, chol() will give you an error for obvious reasons.
I suggest you parametrize directly in terms of the Cholesky decomposition., i.e., Let L be an unknown matrix and set the constraint,
ceq=L*L'-[betas(7) betas(9); betas(9) betas(8)];
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Matt J
Matt J 2022-8-9
Yes, L would be composed of unknowns in addition to beta.
L=[L1,0;
L2,L3];

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更多回答（1 个）

Torsten
Torsten 2022-8-9
It is not guaranteed that the "test parameters" betas satisfy the constraints in each iteration of the optimization process.
So you should first check for positive definiteness before calling Chol. If not, enlarge the diagonal elements artificially by a certain amount.

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