# [R] Solving a quadratically constrained linear program with inital values

Martin Maechler m@ech|er @end|ng |rom @t@t@m@th@ethz@ch
Tue May 18 09:30:07 CEST 2021

>>>>> Bert Gunter
>>>>>     on Mon, 17 May 2021 17:27:27 -0700 writes:

> Have you looked here:
> https://cran.r-project.org/web/views/Optimization.html

yes, he has .. and I've suggested to him to ask here ...

> (Warning: I have no idea whether your query even makes
>  mathematical sense.)

Indeed, it *does* make sense; at least for the case of positive
(semi-)definite \Sigma  which we may well assume for the moment.

Martin Maechler

> Bert Gunter

> "The trouble with having an open mind is that people keep coming along and
> sticking things into it."
> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )

> On Mon, May 17, 2021 at 12:56 PM Pascal Kündig <pascal.kuendig using bluewin.ch>
> wrote:

>> Hi everyone,
>> I'm looking for an R-function that solves a quadratically constrained
>> linear program of the form:
>>
>> min(x) -\mu' x
>> subject to
>> x' \Sigma x <= s
>> 1'x <= 1
>> -1'x <= -1
>> Ix <= u
>> -Ix <= -b
>>
>> while considering a given starting value for the vector x.
>> The above problem results from a larger program of the same structure
>> and by setting the constraint that some elements of the solution vector
>> \tilde{x} of this larger program have to be 0 if they lie below a
>> certain threshold. The starting value for the vector x is therefore a
>> subvector of \tilde{x}. \Sigma is symmetric but not necessarily positive
>> definite.
>>
>> ______________________________________________
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>> and provide commented, minimal, self-contained, reproducible code.
>>

> [[alternative HTML version deleted]]

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