3 papers
math.OC2026
Bilevel gradient methods and the Morse parametric qualification condition
Jérôme Bolte, Quoc-Tung Le, Edouard Pauwels +1
We introduce the Morse parametric qualification condition for bilevel programming. Generic semi-algebraic functions are Morse parametric in a piecewise sense. Thus, bilevel program…
cs.LG2025
Convergence of optimizers implies eigenvalues filtering at equilibrium
Jerome Bolte, Quoc-Tung Le, Edouard Pauwels
Ample empirical evidence in deep neural network training suggests that a variety of optimizers tend to find nearly global optima. In this article, we adopt the reversed perspective…
cs.CC2025
Geometric and computational hardness of bilevel programming
Jérôme Bolte, Quoc-Tung Le, Edouard Pauwels +1
We first show a simple but striking result in bilevel optimization: unconstrained smooth bilevel programming is as hard as general extended-real-valued lower semicontinu…