Perturbation Analysis Of Optimization Problems

By Benjamin Pfaff. 2016

1,250 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Composing graphical models with neural networks for structured representations and fast inference (2016, neutral): “[29] J Frederic Bonnans and Alexander Shapiro.”
OptNet: Differentiable Optimization as a Layer in Neural Networks (2017, neutral): “These techniques also come up in bilevel optimization (Gould et al., 2016; Kunisch & Pock, 2013) and sensitivity analysis (Bertsekas, 1999; Fiacco & Ishizuka, 1990; Bonnans & Shapiro, 2013).”
Generalizing to Unseen Domains via Adversarial Data Augmentation (2018, neutral): “Lemma 4 ([4, Proposition 4.32]) .”
A Conditional Gradient-based Method for Simple Bilevel Optimization with Convex Lower-level Problem (2022, background): “(Bonnans and Shapiro, 2013) (A detailed discussion about this instability issue is provided in Appendix D).”
Delta-method inference for a class of set-identified SVARs (2018, methodology): “280 in the book of Bonnans and Shapiro (2000) present a generalized version of the envelope theorem.”
Second Order Optimality Conditions and Their Role in PDE Control (2015, background): “Readers who are interested in the abstract theory of second order sufficient optimality conditions in infinitedimensional spaces are also referred to the detailed discussion in [6].”
Constrained Learning With Non-Convex Losses (2021, background): “For convex problems, perturbation results can be used to connect the value of ξ to the magnitude of the deviation from P [33], [57].”
Distributionally Robust Optimization: A Review (2019, background): “, Bonnans and Shapiro [55], (2) stability analysis of a SO model with respect to a change in”
Inference for empirical Wasserstein distances on finite spaces (2016, methodology): “Directional Hadamard differentiability We prove our distributional limit theorems by using the theory of parametric programming (Bonnans and Shapiro, 2013) which investigates how the optimal value and the optimal solutions of an optimization problem change when the objective function and the constra”
Efficient and Modular Implicit Differentiation (2021, unknown): “Although implicit differentiation has a long history in numerical analysis [48, 10, 57, 20], so far, it remained difﬁcult to use for practitioners, as it required a case-by-case tedious mathematical derivation and implementation.”
Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm (2019, background): “Therefore, Moreover, since ϕ : D → Z is continuous, there exists η > 0 such that, and hence, it follows from (A.17) that 3 continuously Gâteaux diﬀerentiable function are Fréchet diﬀerentiable [7, pp.34-35].”
Adversarial Robustness with Semi-Infinite Constrained Learning (2021, background): “Further details regarding this result as well as a full proof can be found in [99, Prop.”
Parabolic regularity in geometric variational analysis (2019, methodology): “Let us now recall the notion of C2-cone reducible sets that plays an important role in constrained optimization, especially in its second-order aspects; see Bonnans and Shapiro [7].”
Network Equilibrium of Coupled Transportation and Power Distribution Systems (2018, background): “Local continuity of optimal solution function is studied in [73].”
Distributionally Robust Chance Constrained Optimal Power Flow with Renewables: A Conic Reformulation (2018, unknown): “99 in [51] implies that for any x ∈ Z, infP∈P1 P [|ξ| ≤ T ] = infP∈P1 E[I(|ξ| ≤ T )] can be reformulated as”