CODEWITHSUNDEEP
matlaboptimizationquadratic-programming
user2042145
user2042145

Reputation: 141

symbolic Quadratic optimization using matlab

I am trying to minimize the following expression: U and W are not important you can consider them as I

I am trying to minimize over x given y,x^H and A. with U and W as identity matrix.

I tried fmincon but with no success here is what i did

   [B,C] = fmincon(@(X-OD).'*(X-OD)+(Ycount-A*X).'*(Ycount-A*X),0,[],[],[],[],0,inf)

Any help would be appreciated

Upvotes: 1

Views: 261

Answers (1)

Matthew Gunn
Matthew Gunn

Reputation: 4519

I'm going to ignore the "symbolic" part of the question. To numerically solve this problem, there are two approaches I would recommend:

Use CVX

Download the package CVX. The code would be:

cvx_begin
variables x(n)

minimize(quad_form(x - xh, U_inv) + quad_form(y - A*x, W_inv))
subject to:
x >= 0
cvx_end

Do some math and use Matlab function quadprog

Doing some algebra, you can show your problem is equivalent to:

minimize (over x) .5x'(inv(U) + A'inv(W)*A)x +(-y'*inv(W)*A-xh'*inv(U))*x
      subject to: x>=0

Thse you can use Matlab function quadprog.

H = U_inv + A'*W_inv*A;         %'
f = -y'*W_inv*A - xh'*U_inv;    
Aeq = [];
beq = [];
LB  = zeros(n, 1);
UB  = [];
x_method2 = quadprog(H, f, [], [], Aeq, beq, LB, UB);

Upvotes: 1

Related Questions