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From: Steven Lord on 17 May 2010 13:14

"MZ AM" <mazamin(a)yahoo.com> wrote in message
news:hsrrmo$bd3$1(a)fred.mathworks.com...
> Thanks Matt.
>
> You are right about the way the the constraints should be applied.
> Actually I had defined a function that was called as an argument of
> fmincon and returned [cineq, ceq]. But because in my case cineq is a
> vector itself and ceq=[], I was just showing the cineq in my posting. But
> to clear the confusion of why cineq is a vector, I should mention that the
> optimization should be performed in a range of data that are pressure (p)
> dependent. I would like the optimization use the constraints and read all
> from one constraint function file:
>
> con1 for p<p1
> con2=[ ] for p1<p<p2
> con3 for p>p2

So you have different sets of nonlinear constraints (with different numbers
of constraints) depending on where in the parameter space your parameter's
current value is located? That seems like a Bad Thing.

> So with the above description I will need the cineq to be a vector like:
> cineq=[-0.1 -0.2 .....[] [] []......-0.5 0.15] (and of course these []'s
> cause problem because they are not double-type data). Also in my case
> ceq=[].

No, the problem is not that [] is "not double-type data":

x = [];
whos x

The problem is that you're changing the _number_ of constraints, and that
none of the optimization functions can handle directly.

Either solve the problem in each region (where p < p1, where p is between p1
and p2, and where p2 < p) separately and choose the best result from the
three solutions or keep the length of the cineq vector the same for all the
constraint sets by padding it with 0's.

> On the other hand, I do not want to use three fmincon functions for the
> the three ranges of pressure that I have as it will yield three different
> optimized values which is not desired in my problem.
> I don't believe a vector constraint can cause a problem, do you?

It can if the vector of constarints is not the same size each time.

--
Steve Lord
slord(a)mathworks.com
comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ


From: Matt J on 17 May 2010 13:43

> Either solve the problem in each region (where p < p1, where p is between p1
> and p2, and where p2 < p) separately and choose the best result from the
> three solutions or keep the length of the cineq vector the same for all the
> constraint sets by padding it with 0's.
=================

Probably best to solve the problem in each region separately. If you try to piece together the 3 different constraints by padding cineq with zeros, the constraints will (potentially) be non-differentiable at the boundaries of the three regions, thereby violating the theory underlying fmincon.



> > On the other hand, I do not want to use three fmincon functions for the
> > the three ranges of pressure that I have as it will yield three different
> > optimized values which is not desired in my problem.

Why is that a big deal? Once you have the 3 different solutions, just choose the one with the best objective function value.
From: MZ AM on 19 May 2010 15:58
Thanks Walter,

I executed my code with nonlinear inequality set to +inf. However after about 5 hrs it did not converge and I stopped it (the same program with no constraint converges in about 10sec). But if I want to answer your question about the difference between inf and null constraints I would say that in the latter we want to minimize a function F with no constraint, for example F= x^2 - 1 which gives me x=0 for the entire my entire domain. Now if I set a constraint e.g. x>1, the answer will be x_min=1, if I set x>10, x_min will be 10. But what if x>inf? Will be the x_min=inf acceptable? I guess the answer is no. So I believe that the function does not know what the true constraint is in when constraint is inf.

Thanks
Mazyar

Walter Roberson <roberson(a)hushmail.com> wrote in message <NZWGn.7324$h57.2120(a)newsfe22.iad>...
> MZ AM wrote:
>
> > Basically I do not need any constraint under some numerical
> > circumstances that's why I use null. If I understood you correctly, the
> > use of realmax that you explained may simulate something like infinity
> > for my constraint, which is not correct in my case.
>
> What difference do you perceive between a constraint of infinity and no
> constraint at all? Unless you want that parameter to possibly be complex
> -- I haven't checked to see if fmincon handles complex parameters?
From: Walter Roberson on 19 May 2010 16:04
MZ AM wrote:
> But if I want to answer your
> question about the difference between inf and null constraints I would
> say that in the latter we want to minimize a function F with no
> constraint, for example F= x^2 - 1 which gives me x=0 for the entire my
> entire domain. Now if I set a constraint e.g. x>1, the answer will be
> x_min=1, if I set x>10, x_min will be 10. But what if x>inf? Will be the
> x_min=inf acceptable? I guess the answer is no. So I believe that the
> function does not know what the true constraint is in when constraint is
> inf.

The documentation for fmincon says,

"If x(i) is unbounded below, set lb(i) = -Inf, and if x(i) is unbounded above,
set ub(i) = Inf."


Your argument supposes that the *lower* bound is set to infinity.
From: MZ AM on 19 May 2010 17:50
Thanks Matt.

Could you further elaborate the " If you try to piece together the 3 different constraints by padding cineq with zeros..." ?

I also agree with you about using 3 different equations. But this is not the way that it used to be done. But probably I will give it a shot.

Thanks,
MZ

"Matt J " <mattjacREMOVE(a)THISieee.spam> wrote in message <hsrv79$a6h$1(a)fred.mathworks.com>...
>
> > Either solve the problem in each region (where p < p1, where p is between p1
> > and p2, and where p2 < p) separately and choose the best result from the
> > three solutions or keep the length of the cineq vector the same for all the
> > constraint sets by padding it with 0's.
> =================
>
> Probably best to solve the problem in each region separately. If you try to piece together the 3 different constraints by padding cineq with zeros, the constraints will (potentially) be non-differentiable at the boundaries of the three regions, thereby violating the theory underlying fmincon.
>
>
>
> > > On the other hand, I do not want to use three fmincon functions for the
> > > the three ranges of pressure that I have as it will yield three different
> > > optimized values which is not desired in my problem.
>
> Why is that a big deal? Once you have the 3 different solutions, just choose the one with the best objective function value.
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