Optimization with cost and constraints returned from a single function call

Specific Domains Optimization (Mathematical)
1

I need to solve a constrained non-linear optimization problem where the cost and constraints are computed via a vector-value function. E.g., instead of

J = cost(x)
c1 = constraint1(x)
c2 = constraint2(x)

I have, for efficiency reasons,

J,c1,c2 = myfunc(x)

Do any of the optimizer packages support this?

2

If you are looking for a solver supporting the evaluation of constraints and objective in the same callback, Knitro.jl is a way-to-go (but has a commercial license).

Another way to go is to define the callbacks for your solver (eval_f and eval_cons) in a closure, where you could evaluate the constraints and the objective jointly. For instance:

function buid_callback(x0)
    J, c1, c2 = myfunc(x0)
    current_x = hash(x0)
    function eval_f(x)
        if hash(x) != current_x
            current_x = hash(x)
            J, c1, c2 = myfunc(x)
        end
        return J 
    end
    function eval_cons!(cons, x)
        if hash(x) != current_x
            current_x = hash(x)
            J, c1, c2 = myfunc(x)
        end
        cons[:] = [c1, c2]
    end
            
    return (eval_f, eval_cons)
end
2 Likes
3

Thanks for the heads up on Knitro. I will look into it, but the commercial license will probably be a problem.

I’m not sure I understand your callback example. It looks like myfunc is getting called twice. Once for the objective and once for the constraints.

4

I acknowledge the example is not that self-explanatory. The thing is, by using this closure, you could build you two callbacks suitable, for any optimization solvers:

eval_f, eval_cons = build_callback(x0)

Then, each time you are calling eval_f at a new point x, the function will look if it has already computed this point. If so, it will return the previously stored solution J,c1, c2. Otherwise, it will call your function myfunc.

So imagine that in the solver you are calling eval_f, then eval_cons, on a new point x. Then

  • As x is a new point, you will call myfunc when you first call the function eval_f, and store the result in the cache inside the closure
  • Then, when you call eval_cons at x, the function will recognize that it has already computed myfunc on x and hence will return directly (c1, c2), without recomputing all from scratch
5

Wow, thats cool. I’ve not seen this pattern before. It certainly looks like it’ll do the trick. Thanks for the extra details