Re: Minimize the optimization function

On Nov 21, 10:14 pm, Ray Vickson <RGVick...@xxxxxxx> wrote:
On Nov 21, 5:08 am, nikl...@xxxxxxxxx wrote:

y1*(x1^2) + y2*(x2^2) + .. yn*(xn^2) = C,

The function y1*x1 + y2*x2 + ...+yn*xn should be minimum

y1>y2>....yn  all non-negative integers


This problem was modelled after a cake tower. A cake tower is made of
cylinders of decreasing radius and heights.So they are not equal
otherwise we would be reducing a variable had it been equal .


Had it been y1>= y2 >= ..., will it make the problem easier ? How does
it make it easier.


Do you really mean y1 > y2 > ..., or do you mean y1 >= y2 >= ... ?
The former.

Are the xi variables also, or are they just given input parameters. If
they are variables, are they restricted in sign, or are they free? If
the xi are given parameters, just determining if the problem is
feasible might be non-trivial.

They xi and yi all of them are positive integers. Heights and radius
of cylinders are integers.



how to determine x1,y1,x2,y2...xn,yn ?

Are there any elegant ways to solve this problem without integer
programming ?

If the xi are also variables you have a nonlinear mixed-integer (or
pure integer) program, so the usual integer-programming methods won't
apply. However, methods for handling such problems do exist, although
they are probably not very good yet.

It is a nonlinear mixed-integer.


.