Second-Order Sensitivity Analysis for Bilevel Optimization. (arXiv:2205.02329v1 [math.OC])

Web: http://arxiv.org/abs/2205.02329

In this work we derive a second-order approach to bilevel optimization, a
type of mathematical programming in which the solution to a parameterized
optimization problem (the "lower" problem) is itself to be optimized (in the
"upper" problem) as a function of the parameters. Many existing approaches to
bilevel optimization employ first-order sensitivity analysis, based on the
implicit function theorem (IFT), for the lower problem to derive a gradient of
the lower problem solution with respect to its parameters; this IFT …

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