Is it possible to add more constraints than the default ones in LSQLIN function?

I'm solving a constrained linear least-squares problem using lsqlin. I've specified values for C,d,A,b,Aeq and beq. I used all the default constraints that are included in the solver except for the uper and lower bounds.

x = lsqlin(C,d,A,b,Aeq,beq,lb,ub,x0,options)

A⋅x≤b

Aeq⋅x=beq

I want to add one more constraint to the solver that is different from the above constraints that I already used, Is there a way to specify more constraints in addition to the ones that are by default in the solver?

Any help is appreciated!

[Torsten]

Don't you think we need to know the constraint you want to impose in order to be able to give advice ?

[John D'Errico]

There are no default constraints. And you can supply more than one constraint. That is, A and Aeq can be MATRICES, with b and beq being vectors. That means A can have as many rows as you wish, with each row being another constraint. The same applies to Aeq.

[HN]

Thanks for your reply @John D'Errico @Torsten. I have C as matrix of size 8x5. d is a column vector of size 8x1.

My first constraint is A⋅x≤b where A is equal to C and b is a column vector equal to 0.9.*d.

The second constraint is Aeq⋅x=beq where Aeq is matrix of 4x5 and beq is a column vector of zeros of size 4x1.

x will be obtained from the optimizer and it will be of size 5x1

After obtaining x from the optimizer, I'm calculating a new column d_new where d_new=C*x. It will have the same size as d.

I wanted to add an additional constraint in the optimizer that assures that each element in d_new has the same sign as its repective value in d.

Hope it's clearer!

Answer 1

[Matt J]

You can still use lsqlin, but as John said, you can add additional inequality constraints as follows,

Q=-sign(d).*C;
r=zeros(size(d));

Aineq=[A;Q]
bineq=[b;r];

x = lsqlin(C,d,Aineq,bineq,Aeq,beq,lb,ub,x0,options)

[HN]

It works! Thank you for your help.

Answer 2

[Torsten]

Use "fmincon" with the constraint (C*x).*d >=0 and define this constraint in function "nonlcon".

[HN]

This is useful. Thank you!