fmincon

If the matrix Aeq in linear constraint Aeq*x=beq have parameters，how can this kind of problem be solved using the function fmincon to obtain the optimized parameters in matrix A？

Answer 1

[Titus Edelhofer]

Hi Ashley,

do I understand correctly: there are two entries in Aeq which you want to optimize as well? In this case Walter is right: you would need to put into the non linear constraint function (and add to the variables), i.e., your x will be in fact [x_1,...,x_n,A_1,A_2], where A_1 and A_2 do nothing in the objective function, but will be used in the constraint function (something like)

function [c,ceq] = mynonlin(xAll)
x = xAll(1:end-3);
Aeq = [1 xAll(end-1); 0 xAll(end)]; % example
beq = ...;
ceq = Aeq*x-beq;

Titus

[Walter Roberson]

Lower bound should be passed in as the 7th parameter of fmincon, lb. Use 0 for lb(K) if the K'th parameter is to have a lower bound of 0. Use -inf as a place holder for any parameter which is not to have a lower bound.

Upper bounds go in to the 8th parameter; use +inf as a placeholder for any parameter which is not to have an upper bound.

Use [] as the vector of bounds if none of the parameters have that kind of bound.

[Ashley]

Thanks for the information.I have got the result and found an interesting phenomenon：the optimized object dependent on the lower bounds of the two parameters in the matrix.

I greatly appreciate your help!Thans so much!

Answer 2

[Chirag Gupta]

I would start with typing doc fmincon for the documentation on the function.

It might be easier to use optimtool to get started.

[Ashley]

I had checked the help and other materials on the subject but all are telling that the matri A should not be a function with parameters but a matrix with definite value.

And I don't have the optimtool in the start file and I don't know why.I have asked this question at other places but have no answers yet.

Thank you all the same for help!

Answer 3

[Walter Roberson]

If you need to provide parameters instead of definite matrices for Aeq, then fmincon() is not appropriate for your purposes.

What kind of parametrization are you hoping to do?

[Ashley]

The object function subject to linear constraints A*x=B is in nonlinear least-square form.And x has a lower bonud which needs x≥0.The problem is there are 2 parameters in the matrix A and I want to obtain the optimized set of parameters also the vector x which minimize the object function.

[Walter Roberson]

Is there a reason this could not be checked in the non-linear constraint function ?

[Ashley]

What do you mean by saying that？I really can not understand you.

Maybe I didn't describ my problem clearly so you could not understand my problem fully.

My object function is min f(x)=∑(x(i)-x(i+1))^2,which is sum of a series of squares,and the object function only subject to linear constraints Aeq*x=beq，and the matrix Aeq has 2 parameters which I want to optimize.

If fmincon is not appropriate ,which function do you think is better then?

Your help is greatly appreciate！Thanks so much！