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RE: dynamic optimization

• To: mathgroup at smc.vnet.net
• Subject: [mg35291] RE: [mg35268] dynamic optimization
• From: "DrBob" <majort at cox-internet.com>
• Date: Sat, 6 Jul 2002 05:45:23 -0400 (EDT)
• Reply-to: <drbob at bigfoot.com>
• Sender: owner-wri-mathgroup at wolfram.com

Log should have a square bracket after it, not a parenthesis, and the
matching parenthesis isn't there anyway.  So... we can't tell what your
objective function is.

That constraint doesn't appear to be a differential equation.  A
difference equation, maybe... or maybe not.

Are S and C functions?  If so, they need brackets, not parentheses.  If
C is a function, what is its argument in the objective function?

Do you have initial conditions for S and C?

If pi, w, and L are constant functions, why complicate things in the
objective function and constraint equations?

Is P(t) == t, or just 1?  Or something else?

I see W in the constraint equation, and you've defined w(t)=4.  Is there
a connection?

In "Ct/1+..." do you mean "Ct/(1+..."?

In general, I can't tell what the problem is.

Bobby

-----Original Message-----
From: anna in the sky [mailto:annainthesky at mac.com] 
To: mathgroup at smc.vnet.net
Subject: [mg35291] [mg35268] dynamic optimization

Hi,

hopefully somebody is able to help me with this (probably pretty easy )
thing:
I need to do a dynamic maximization over a couple of periods, where the
objective function is nonlinear, and the constraint is linear
differential
equation. The problem looks like this and I tried some things but dont
know
how to solve it actually

objective function: U:= Exp[-rho*t]*Log(Ct/1+(S(t)*P-4C(t))^2
constraint: Constr:= (S(t+1)-S(t))*P(t)+C(t)= = W(t)*L(t)+pi(t)*S(t)*P
where P=1
rho=0.6
pi(t)=0.03
w(t)=4
L(t)=10
the given values can actually be something else, too.
We seek C and S.
does anyone have an idea how to fix this? Just a idea, hint or anything,
I
would be more than glad :)

Thanks
//anna