Quadratic programming with just one constraint

Hi,

I have a quadratic programming problem which basically looks like

I am using quadprog: https://www.mathworks.com/help/optim/ug/quadprog.html#d123e128542

However, the equality restrictions there are only in the form , and the programm demands the matrix to be of full rank. The only constraint I want to impose is , but I don't know how to do this, since apparently I would need as many linear constraints as the . Is there a way around this?

[Matt J]

the programm demands the matrix to be of full rank.

No idea why you think so.

[diego soler polo]

I tried defining $A_eq$ as ones(d) and $b_eq$ as N*ones(1,d) (d is the dimension of my space), so that every constraint equation would be a copy of the only restriction I want, and I got the following error message:

error: quadprog: equality constraint matrix must be full row rank

Answer 1

[Matt J]

We may have to be given your input matrices to reproduce the problem, but since ones(1,d) is full row rank, there shouldn't have been a problem, even if it were a requirement of quadprog. As you can see in the simple example below, no errors are thrown using Aeq=ones(1,d=4):

A=rand(4); A=A*A.'; %symmetrize
c=rand(4,1);

Aeq=ones(1,4); beq=4;
lb=c*0; ub=c*0+10;

quadprog(A,c,[],[],Aeq,beq,lb,ub)

Minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

ans = 4×1

0.0000 0.0000 3.4558 0.5442

[diego soler polo]

Thank you. Yes, that worked. I misunderstood the notation in the reference. It works just fine.