[Ipopt] quadratic programming

Andreas Waechter andreasw at watson.ibm.com
Mon Sep 15 09:40:22 EDT 2008

Hi Anand,

In general, Ipopt can solve quadratic optimization problems.

However, if in your case H is really the identity matrix, you can solve 
this problem by hand.  In this particular case, the problem is separable, 
i.e., it is something like

min sum_i x_i^2 + f_i*x_i
s.t.      lb_i <= x_i <= ub_i   (for all i)

Since one x_i variable "does not influence any other", you can simply 
write a number of one-dimensional problems

min   x_i^2 + f_i*x_i
s..t  lb_i <= x_i <= ub_i

and solve them analytically one after the other.

Hope this helps,


On Mon, 15 Sep 2008, Anand wrote:

> Hi
> Over the last 3 days I have been searching the internet for a open source
> quadratic programming library in c/c++
> My problem is:
> minimize xHx' + xf
> subject to:
> lb <= x <= ub
> where H is an identity matrix and hence sparse for large dimensions
> x is a vector
> lb and ub are the lower and upper bounds respectively on the vector x
> Does ipopt solve such a problem
> Please tell me if you have any open source c/c++ library
> Also if possible give me suggestions as to what algorithms may be able to
> solve these algorithms
> Thanks
> Regards
> Anand

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