Using maximum of optimisation variable as an upper bound for another variable

Hello

I am trying to minimise a cost function where the investment cost is the the maximum value of an optimisation variable multiplied by the cost e.g.

Total cost=Cost per kW*MaxkW

However, matlab doesn't seem to like using an optimisation variable as a boundary condition.

Any solutions?

Thanks

Michael

Answer 1

[Matt J]

Solve N different sub-problems

for j=1:N

  prob.Constraint.TotalCost = sum(x)=CostPerkW*x(j);
 
  prob.Constraint.Max  =  x(j)>=x; %x(j) is the maximum
  
  [X{j} Cost{j}]=solve(prob)
 
end

and take the X{j} with the lowest Cost{j}.

Answer 2

[Ted Shultz]

you can do a bounded obtimization using this file from filecentral: fminsearchbnd

Answer 3

[Bruno Luong]

Not sure what you mean by "boundary condition" (there is no such thing in all optimization frameworks as far as I know), but take a look at fminmax

Answer 4

[Naveen Venkata Krishnan]

Hello Micheal,

Based on the question, I understood the problem in this way , please correct me if am wrong :

"You want to minimize a cost function in such a way that optimization variable lies close to its upper boundary region ".

If this the requirment one way to do it to confine the search space of the optimizer close to upper boundary ( like giving the values of upper - ub and lower boundary - lb of the optimzation variable around the maximum value of the optimization variable ) .

Another way is by using an enforcement operator, i think the following IEEE paper may be of some help to you reg this.

https://ieeexplore.ieee.org/document/537964

Answer 5

[Michael-Allan Millar]

Thanks very much for the help, everyone.

Basically, it's sizing a tank and heat pump. So the bigger the tank, the lower the operating cost but greater initial investment. I ended up doing it the way Matt J suggested, but was hoping there would be a way to give a single answer, rather than having to produce a list then manually picking the smallest cost.

Thanks again!

Michael

[Matt J]

Well, you don't have to "manually" pick. You would just do

[~,jmin]=min([Cost{:}]);

x=X{jmin};