Linear optimization with quadratic constraints
Small example code to set up the problem? JN
On 2017-01-07 06:26 AM, Preetam Pal wrote:
Hi Guys, Any help with this,please? Regards, Preetam On Thu, Jan 5, 2017 at 4:09 AM, Preetam Pal <lordpreetam at gmail.com> wrote:
Hello guys, The context is ordinary multivariate regression with k (>1) regressors, i.e. *Y = XB + Error*, where Y = n X 1 vector of predicted variable, X = n X (k + 1) matrix of regressor variables(including ones in the first column) B = (k+1) vector of coefficients, including intercept. Say, I have already estimated B as B_hat = (X'X)^(-1) X'Y. I have to solve the following program: *minimize f(B) = LB* ( L is a fixed vector 1 X (k+1) ) such that: *[(B-B_hat)' * X'X * (B-B_hat) ] / [ ( Y - XB_hat)' (Y - XB_hat) ] * is less than a given value *c*. Note that this is a linear optimization program *with respect to B* with quadratic constraints. I don't understand how we can solve this optimization - I was going through some online resources, each of which involve manually computing gradients of the objective as well as constraint functions - which I want to avoid (at least manually doing this). Can you please help with solving this optimization problem? The inputs would be: - X and Y - B_hat - L - c Please let me know if any further information is required - the set-up is pretty general. Regards, Preetam