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984. A smoothing barrier augmented Lagrangian gradient-based method for constrained bilevel programs

Invited abstract in session WD-41: Nonsmooth optimization algorithms II, stream Nonsmooth Optimization.

Wednesday, 14:30-16:00
Room: 97 (building: 306)

Authors (first author is the speaker)

1. Mengwei Xu
Institute of Mathematics, Hebei University of Technology

Abstract

Gradient-based methods are known for their efficiency in solving unconstrained bilevel programs. However, when dealing with constrained bilevel programs, the application of this method becomes challenging due to the strict complementarity condition required for the continuous differentiability of the lower level solution mapping within the Karush-Kuhn-Tucker system. To tackle the lower level problem with inequality constraints without relying on strict complementarity, we propose a family of smoothing functions to approximate the primal-dual solution mapping based on the smoothing barrier augmented Lagrangian function, which ensures the preservation of the continuously differentiability and the convexity of the lower level problem. By approximating the bilevel program as single-level constrained problems, we adopt a hybrid approach that combines the gradient-based method with the augmented Lagrangian method. This allows us to effectively solve the constrained bilevel programs. We prove that any accumulation point generated by the algorithm is a Clarke stationary point of the bilevel problem. Importantly, unlike conventional smoothing function methods, the accumulation point can also be a Bouligand stationary point under an additional verifiable condition.

Keywords

Status: accepted

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