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Subject: Re: Integer solutions for a_1*x_1+a_2*x_2+a_3*x_3+ ...+a_4*x_n = k
Date: Tue, 18 Nov 2008 16:27:01 +0000 (UTC)
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> Thereafter, the m-th state transition is from s_(m-1) to s_m=s_(m-1)-a_m*k_m also with cost 0.

Sorry, this should be s_(m-1) to s_m=s_(m-1)-a_m*x_m

Note also that the decision variables will be restricted to 1<=x_m<=k

> After n decisions you will have a terminal cost equal to s_n, which is the residual amount
> 
> a_1*x_1+a_2*x_2+a_3*x_3+ ...+a_4*x_n - k

And this should be

k-a_1*x_1+a_2*x_2+a_3*x_3+ ...+a_4*x_n

....But hopefully you get the idea