Questions tagged [bilevel-optimization]

For questions related to optimization problems in which one decision maker (the "leader") chooses decision variables, then a second decision maker (the "follower") chooses decision variables in response. The optimization problem is formulated from the leader's point of view and takes into account the follower's best response. Bilevel optimization is closely related to Stackelberg games.

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2 votes
1 answer

Interchange upper- and lower-level decision variables in bi-level programming

Consider a general bi-level programming as follows: \begin{align*} \min_{x\in X,y\in Y}&~F(x,y) \\ s.t.&~ G(x,y) \leq 0, \\ &~ y\in \arg\min_{z\in Y}\{f(x,z): ...
13 votes
1 answer

Integrality gap in bilevel binary linear programming problem

I have a bilevel max-min optimization problem over binary variables, with constraints expressed using linear inequalities. The inner (minimization) problem is $$ \begin{alignat}2 \min\limits_x&\...
-3 votes
1 answer

Ask for suggestions on bilevel optimization question [closed]

Here is a bilevel question: the master problem is $\max_y \sum_{n \in 1,...,N} x[n] * y[n];$ subject to $$\min_x \sum_{n \in 1,...,N} x[n] * y[n]$$ $$yy^T = I$$ and some other linear constraints. So ...
3 votes
1 answer

A tricky Bi-Level Location Problem using VISUM

I'm writing my thesis on the optimal location of Air-Taxi Stations. I'm using PTV VISUM for the transport model where I'll inherit the Origin-Destination demand matrix. I come from transportation ...
3 votes
0 answers

How to linearize a max min objective function?

Let us suppose that I have a $\max \min$ objective function that only depends on one set of variables: $\underset{x}\max \underset{y}\min dy$ Associated with the linear set of constraints and right ...
10 votes
1 answer

Is it possible (or straightforward) to define many secondary problems in bilevel programming?

I am new to bilevel programming. I was wondering whether it is possible (or straightforward) to formulate a bilevel problem in which there are many secondary-level problems? An example might be a ...