Re: how to solve this kind of optimization problem
- From: spellucci@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (Peter Spellucci)
- Date: Mon, 22 Oct 2007 09:25:58 +0000 (UTC)
In article <1193022469.259298.26040@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Sam <hollowspook@xxxxxxxxx> writes:
Hi, there.
I wish I can find some help in this forum.
First I have an optimization problem as follows.
min f(x[1], x[2], x[3], x[4],..., x[99], x[100])
s.t. h(x[1], x[2], x[3], x[4],..., x[99], x[100]) = 0;
g-<g(x[1], x[2], x[3], x[4],..., x[99], x[100]) <g+;
x-<x[i]<x+, i =1, 2, 3,..., 100;
This can be solved by interior-point method.
However suppose that there is a new constraint on x now.
sum(k(x[i],x[i+1]))<=50; i = 1, 2, 3,...99;
where k(x[i],x[i+1])=0 if x[i]~=x[i+1] and k(x[i],x[i+1])=0 if
x[i]==x[i+1]
something is a misprint here
maybe you meant "=1" if x[i] not= x[i+1]
? no x[i] should currently change by more than 50 or the total sum?
anyway: a discontinuous constraint like your cannot be used within
nonlinear optimizeers which not only assume continuity but even
C2 - smoothness (otherwise they might terribly fail)
if you want to avoid a too large change in the current x[i]
- whatever its value might be in the given bounds - then you
could do this only by going into the code:
an trust region optimizer would allow this by setting the maximum
trust region radius -
or you could for example try
sqrt ( sum( (x[i]-x[i+1])^2 ) ) <= 50
this is also unsmooth by only on the diagonal in R^n, so its not quite
probable that this will have a bad influence
.
The physical meaning of this new constraint is that we expect the
change on x[i] is less than a constaint value, which is 50 in this
example.
How to deal with this new constraint? Can this new optimization
problem still be solved by interior point method? Please do me a
favour.
Thanks in advance.
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