[R] Linear optimization with quadratic constraints

ProfJCNash profjcnash at gmail.com
Sun Jan 8 15:02:49 CET 2017

```Small example code to set up the problem?

JN

On 2017-01-07 06:26 AM, Preetam Pal wrote:
> Hi Guys,
> 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
>>
>> 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).
>>
>>
>> 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
>>
>
>
>

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