论文标题
高斯 - 纽顿型方法用于双杆优化的方法
Gauss-Newton-type methods for bilevel optimization
论文作者
论文摘要
本文研究了高确定系统的高斯 - 纽顿型方法，以找到解决双重编程问题的解决方案。为了进行，我们使用较低级别的价值功能重新重新重新重新制定，并在适当的假设下考虑必要的最佳条件。首先，在严格的上层和低级可行性约束下，我们证明了高斯 - 纽顿型方法在计算额外可拖动资格条件下满足这些最佳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，从而导致替代方案，例如伪或平滑的高斯 - 牛顿型方法，以进行双光线优化。我们的数值实验是在最近发布的双层优化库（BOLIB）的124个示例上进行的，该实验比较了我们在不同方案下方法的性能，并表明这是解决连续变量的双重优化问题的可拖动方法。
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.
