Thread Subject: what is the category of this problem: linear objective function with quadratic constraints

Hello,

I run into a problem with a linear objective function and a mix of constraints:

one quadratic constraints; others are all linear inequality.

Is there any specific definition in optimization for this type of problem?

Thanks,
Hong

specifically, the problem is defined as:

obj: min/max f = ax1 + bx2 + cx3 + d
s.t:
p2 < c1x1^2+c2x2^2 + c3x1x2 + c4x1 + c5x2 + d1 < p1

c6x1+ c7x2< p3
c8x1 + c9x2<p4
p5<x1<p6
p7<x2<p8

Matlab is able to solve this problem. But I want to know some theory about this problem (if exist) so that it is able to develop some real time algo.

"Hong" <honghaot@gmail.com> wrote in message <hj5sn7$qgs$1@fred.mathworks.com>...
> Hello,
>
> I run into a problem with a linear objective function and a mix of constraints:
>
> one quadratic constraints; others are all linear inequality.
>
> Is there any specific definition in optimization for this type of problem?
>
> Thanks,
> Hong

It seems that your problem (generically) does not have a solution. Note that x3 does not appear in any constraint. Thus, assuming there is a feasible point, and that the constant c in the cost functional is not zero, then the cost can be made arbitrarily small (-\infty) and arbitrarily large (+ \infty).

What 'solution' does Matlab provide ?


"Hong" <honghaot@gmail.com> wrote in message <hj5tds$aec$1@fred.mathworks.com>...
> specifically, the problem is defined as:
>
> obj: min/max f = ax1 + bx2 + cx3 + d
> s.t:
> p2 < c1x1^2+c2x2^2 + c3x1x2 + c4x1 + c5x2 + d1 < p1
>
> c6x1+ c7x2< p3
> c8x1 + c9x2<p4
> p5<x1<p6
> p7<x2<p8
>
> Matlab is able to solve this problem. But I want to know some theory about this problem (if exist) so that it is able to develop some real time algo.
>
> "Hong" <honghaot@gmail.com> wrote in message <hj5sn7$qgs$1@fred.mathworks.com>...
> > Hello,
> >
> > I run into a problem with a linear objective function and a mix of constraints:
> >
> > one quadratic constraints; others are all linear inequality.
> >
> > Is there any specific definition in optimization for this type of problem?
> >
> > Thanks,
> > Hong

Gene, you are right. I doesn't define the problem correctly. Actually, x3 have boundary. therefore, the problem should be:

> > obj: min/max f = ax1 + bx2 + cx3 + d
> > s.t:
> > p2 < c1x1^2+c2x2^2 + c3x1x2 + c4x1 + c5x2 + d1 < p1
> >
> > c6x1+ c7x2< p3
> > c8x1 + c9x2<p4
> > p5<x1<p6
> > p7<x2<p8
      p9<x3<p10

the matlab will give me the right result. The question is that realtime algo is needed. Matlab is too large to realtime system.

"Gene" <ecliff@vt.edu> wrote in message <hj7791$i1$1@fred.mathworks.com>...
> It seems that your problem (generically) does not have a solution. Note that x3 does not appear in any constraint. Thus, assuming there is a feasible point, and that the constant c in the cost functional is not zero, then the cost can be made arbitrarily small (-\infty) and arbitrarily large (+ \infty).
>
> What 'solution' does Matlab provide ?
>
>
> "Hong" <honghaot@gmail.com> wrote in message <hj5tds$aec$1@fred.mathworks.com>...
> > specifically, the problem is defined as:
> >
> > obj: min/max f = ax1 + bx2 + cx3 + d
> > s.t:
> > p2 < c1x1^2+c2x2^2 + c3x1x2 + c4x1 + c5x2 + d1 < p1
> >
> > c6x1+ c7x2< p3
> > c8x1 + c9x2<p4
> > p5<x1<p6
> > p7<x2<p8
> >
> > Matlab is able to solve this problem. But I want to know some theory about this problem (if exist) so that it is able to develop some real time algo.
> >
> > "Hong" <honghaot@gmail.com> wrote in message <hj5sn7$qgs$1@fred.mathworks.com>...
> > > Hello,
> > >
> > > I run into a problem with a linear objective function and a mix of constraints:
> > >
> > > one quadratic constraints; others are all linear inequality.
> > >
> > > Is there any specific definition in optimization for this type of problem?
> > >
> > > Thanks,
> > > Hong