fmincon nonlinear inequality constraint

Question

hey yo 2022-8-9

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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:

beta(7)>0
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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Answer 1

Matt J 2022-8-9

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https://ww2.mathworks.cn/matlabcentral/answers/1776400-fmincon-nonlinear-inequality-constraint#answer_1023605

编辑：Matt J 2022-8-9

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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)];