This article studies Gauss–Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary optimality conditions under appropriate assumptions. First, under strict complementarity for upper- and lower-level feasibility constraints, we prove the convergence of a Gauss–Newton-type method in computing points satisfying these optimality conditions under additional tractable qualification conditions. Potential approaches to address the shortcomings of the method are then proposed, leading to alternatives such as the pseudo or smoothing Gauss–Newton-type methods for bilevel optimization. Our numerical experiments conducted on 124 examples from the recently released Bilevel Optimization LIBrary (BOLIB) compare the performance of our method under different scenarios and show that it is a tractable approach to solve bilevel optimization problems with continuous variables.

本文研究超定系统的高斯-牛顿型方法，以找到双层编程问题的解决方案。为了继续进行，我们使用双层程序的低级值函数重构，并在适当的假设下考虑必要的最优性条件。首先，在上下级可行性约束的严格互补下，我们证明了高斯-牛顿型方法在满足附加最优条件条件的条件下满足这些最优性条件的计算点的收敛性。然后提出了解决该方法缺点的潜在方法，从而导致了替代方案，例如伪或平滑高斯-牛顿型方法进行了双层优化。