257. Interior point method based on the optimal value function for bilevel optimization problems
Invited abstract in session FB-5: Recent advances in bilevel optimization II, stream Bilevel optimization: strategies for complex decision-making.
Friday, 10:05 - 11:20Room: M:N
Authors (first author is the speaker)
| 1. | Yasushi Narushima
|
| Department of Industrial and Systems Engineering, Keio University | |
| 2. | Seima Yamamoto
|
| Keio University |
Abstract
The bilevel optimization problem has upper-level and lower-level optimization problems. First, the upper-level problem is solved and then the lower-level problem is solved; the two problems are interrelated. To develop an efficient algorithm for solving the bilevel optimization problem, we apply the interior point method to the bilevel optimization problem. Because the method is effective for nonlinear optimization problems, we expect that the interior point method for the bilevel optimization problem will also be efficient. First, we derive the optimality conditions using the optimal value function because more manageable optimality conditions can be obtained than those that use the KKT conditions of the lower-level problem. Based on these optimality conditions, we propose an interior point method that guarantees local convergence. Additionally, by modifying this algorithm, we propose an interior point method that ensures global convergence. In this algorithm, we use the squared L2-norm of the shifted KKT condition as a merit function because the values of the optimal value function cannot be expressed explicitly. Moreover, by refining the calculation of step sizes, we ensure interior points and guarantee global convergence. Finally, some numerical results are given to confirm the effectiveness of the proposed algorithm.
Keywords
- Multilevel optimization
Status: accepted
Back to the list of papers