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The adjoint state method for parametric definable optimization without smoothness or uniqueness
Jérôme Bolte, Edouard Pauwels, Cheik Traoré
We establish that nonconvex definable parametric optimization problems with possibly nonsmooth objectives, inequality constraints, conic constraint systems, and non-unique primal a…
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…
Derivatives of Stochastic Gradient Descent in parametric optimization
Franck Iutzeler, Edouard Pauwels, Samuel Vaiter
We consider stochastic optimization problems where the objective depends on some parameter, as commonly found in hyperparameter optimization for instance. We investigate the behavi…
Inexact subgradient methods for semialgebraic functions
Jérôme Bolte, Tam Le, Éric Moulines +1
Motivated by the extensive application of approximate gradients in machine learning and optimization, we investigate inexact subgradient methods subject to persistent additive erro…