quadprog vs fmincon

I have this minimization problem: to minimize f(x)=x'*A*x under the constraints x'*C{j}*x=g{j}, j=1,2,...,J; Both obj function and the constraints are quadratic (A'=A and C{j}'=C{j}), it is obviously more advantageous to use a quadratic programming routine. However as far as I checked, quadprog only accepts linear equality constraints. Is there any way around or do I have to go to fmincon? The problem with fmincon here is J is fairly large and the gradient of constraint is therefore a very large matrix of N by J, where N is the length of x. The N by J gradient matrix is sort of sparse but it is tedious to keep track of all the indices, instead, I can provide multiplication function handle for this matrix with fast algorithm (fft), but fmincon doesn't seem to accept that. Is there any way around that? Any suggestions or comments are welcome, thank you.

Jin

Answer 1

[Rakesh Kumar]

Have you looked at fmincon 'interior-point' algorithm option? Here is a snippet of help from this algorithm

W = HessMultFcn(x,lambda,v);

The result W should be the product H*v, where H is the Hessian at x, lambda is the Lagrange multiplier (computed by fmincon), and v is a vector.

Hth, Rakesh