Hi Morteza;

in general you can not do that. It tightly depend on your leader and follower. Consider the following example: lets say x belongs to {1, 2} and y belongs to {1, 2}. Also lets say f(x, y) is defined as: f(1,1)=1, f(1,2)=4, f(2,1)=3, f(2,2)=2. Also, g(x, y) is defined as g(1,1)=3, g(1,2)=5, g(2,1)=4, and g(2,2)=1. The optimal solution when f is the leader is 1 and x=1, y=1 (note that g(1,1) is the optimal choice for g when x=1). However, the optimal solution when g is the leader is x=2, y=2 (note that when y is 2, the optimum solution for f as the follower is x=2 and f(2,2)=2). This means that you can not exchange the follower and leader IN GENERAL CASE. But it might be possible to do that under specific conditions for f and g.

Dear Mohammad-Reza,

Many thanks for your fruitful answer. Although I got a unique result for a typical bilevel optimization problem by swapping its upper-level with the lower-level,however, as you mentioned, it is not possible in general.

As a matter of fact, it was a question to think.

Once again, I am really grateful to you for your helpful response.

Regards,

Morteza Shabanzadeh

if the problem is asynchronous, you cannot.

Dear Alireza,

Many thanks for your answer. I would like to know that how I can realize the bi-level problem is synchronous or asynchronous?

I swapped upper-level and lower-level in a simple problem and got the same solution!

I look forward to reading your helpful answer.

Regards,

Morteza

Dear Morteza,

Sorry for a delayed comment.

In any bilevel problem with independent objectives, they can be swept. Like the following simple example:

Min J(x) = x1^2 + a x2^2

s.t.

a = argmax(a - 2a^2)

But then it is not a bilevel problem! :-)