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Thread Subject:
Optimization problem

Subject: Optimization problem

From: S

Date: 26 Oct, 2011 11:10:31

Message: 1 of 4

Hi,

I have 2 equations:
max... S = ( (j) / (j + 0.5*w) )^2 [Eqn 1]
min... x = (const) * (j / w) [Eqn 2]

I would like to find j and w when: S is a maximum and x is a minimum.

I have 2 equations, with 4 unknowns: S,x,j,w.

Are there any matlab algorithms (perhaps in the optimization toolbox) that will let me do this?

w and j are bounded:
1e-6 < w < 1e-3
10e-6 < j < 1e-3

S and x are bounded:
0 <= S <= 1
0 < x <= 10

*Note: the bounds are just a rough estimate.

Any ideas?

Subject: Optimization problem

From: pietro

Date: 26 Oct, 2011 12:07:24

Message: 2 of 4

"S" wrote in message <j88pr7$rg3$1@newscl01ah.mathworks.com>...
> Hi,
>
> I have 2 equations:
> max... S = ( (j) / (j + 0.5*w) )^2 [Eqn 1]
> min... x = (const) * (j / w) [Eqn 2]
>
> I would like to find j and w when: S is a maximum and x is a minimum.
>
> I have 2 equations, with 4 unknowns: S,x,j,w.
>
> Are there any matlab algorithms (perhaps in the optimization toolbox) that will let me do this?
>
> w and j are bounded:
> 1e-6 < w < 1e-3
> 10e-6 < j < 1e-3
>
> S and x are bounded:
> 0 <= S <= 1
> 0 < x <= 10
>
> *Note: the bounds are just a rough estimate.
>
> Any ideas?

Hi,

you can change your problem in this way:
min... S =-1* ( (j) / (j + 0.5*w) )^2 [Eqn 1]
min... x = (const) * (j / w) [Eqn 2]

and then use a multiobjective routine. As alternative you can search the min of S+x.

Best regards

Pietro

Subject: Optimization problem

From: S

Date: 26 Oct, 2011 13:47:30

Message: 3 of 4

"pietro " <bracardi82@email.it> wrote in message <j88t5s$82e$1@newscl01ah.mathworks.com>...
> "S" wrote in message <j88pr7$rg3$1@newscl01ah.mathworks.com>...
> > Hi,
> >
> > I have 2 equations:
> > max... S = ( (j) / (j + 0.5*w) )^2 [Eqn 1]
> > min... x = (const) * (j / w) [Eqn 2]
> >
> > I would like to find j and w when: S is a maximum and x is a minimum.
> >
> > I have 2 equations, with 4 unknowns: S,x,j,w.
> >
> > Are there any matlab algorithms (perhaps in the optimization toolbox) that will let me do this?
> >
> > w and j are bounded:
> > 1e-6 < w < 1e-3
> > 10e-6 < j < 1e-3
> >
> > S and x are bounded:
> > 0 <= S <= 1
> > 0 < x <= 10
> >
> > *Note: the bounds are just a rough estimate.
> >
> > Any ideas?
>
> Hi,
>
> you can change your problem in this way:
> min... S =-1* ( (j) / (j + 0.5*w) )^2 [Eqn 1]
> min... x = (const) * (j / w) [Eqn 2]
>
> and then use a multiobjective routine. As alternative you can search the min of S+x.
>
> Best regards
>
> Pietro

Thanks for the reply and help.

Any particular function you recommend?

Subject: Optimization problem

From: pietro

Date: 27 Oct, 2011 08:17:17

Message: 4 of 4

"S" wrote in message <j8931i$sep$1@newscl01ah.mathworks.com>...
> "pietro " <bracardi82@email.it> wrote in message <j88t5s$82e$1@newscl01ah.mathworks.com>...
> > "S" wrote in message <j88pr7$rg3$1@newscl01ah.mathworks.com>...
> > > Hi,
> > >
> > > I have 2 equations:
> > > max... S = ( (j) / (j + 0.5*w) )^2 [Eqn 1]
> > > min... x = (const) * (j / w) [Eqn 2]
> > >
> > > I would like to find j and w when: S is a maximum and x is a minimum.
> > >
> > > I have 2 equations, with 4 unknowns: S,x,j,w.
> > >
> > > Are there any matlab algorithms (perhaps in the optimization toolbox) that will let me do this?
> > >
> > > w and j are bounded:
> > > 1e-6 < w < 1e-3
> > > 10e-6 < j < 1e-3
> > >
> > > S and x are bounded:
> > > 0 <= S <= 1
> > > 0 < x <= 10
> > >
> > > *Note: the bounds are just a rough estimate.
> > >
> > > Any ideas?
> >
> > Hi,
> >
> > you can change your problem in this way:
> > min... S =-1* ( (j) / (j + 0.5*w) )^2 [Eqn 1]
> > min... x = (const) * (j / w) [Eqn 2]
> >
> > and then use a multiobjective routine. As alternative you can search the min of S+x.
> >
> > Best regards
> >
> > Pietro
>
> Thanks for the reply and help.
>
> Any particular function you recommend?

fmincon, look at the manual!

Pietro

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