Optimization Problems with Perturbations: A Guided Tour

By J. Bonnans, Alexander Shapiro, J. Fr Ed Eric Bonnans. 1998

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Citations in the corpus

Lifelong Policy Gradient Learning of Factored Policies for Faster Training Without Forgetting (2020, methodology): “To prove Part A, we apply a corollary to Theorem 4.1 in [4].”
More efficiency in multiple kernel learning (2007, background): “Di.erentiability issues and derivatives computation of optimal values of optimization problems have been largely discussed by Bonnans and Shapiro (1998).”
Does Distributionally Robust Supervised Learning Give Robust Classifiers? (2016, methodology): “We ﬁrst review Proposition 1 by Bartlett et al. (2006) and Tewari & Bartlett (2007) that justiﬁes the use of classiﬁcation-calibrated losses in ERM for classiﬁcation.”
ELLA: An Efficient Lifelong Learning Algorithm (2013, methodology): “…Lipschitz on the space of latent model components L. Proof sketch: Part (A) can be easily shown using the fact that α is continuous and by applying a corollary of Theorem 4.1 as stated by Bonnans & Shapiro (1998) ELLA: An Efficient Lifelong Learning Algorithm (originally shown by Danskin (1967)).”
Characterizations of Lipschitzian Stability in Nonlinear Programming (2020, background): “For recent surveys also on other aspects of the subject, see [4] and [15].”
Online dictionary learning for sparse coding (2009, methodology): “Then, a classical theorem from perturbation theory ( Bonnans & Shapiro, 1998, Theorem 4.1) shows that l(x, D) is C 1 . This, allows us to use a last result on empirical processes ensuring that f(Dt) − ˆ ft(Dt) converges almost surely to 0. Therefore f(Dt) converges as well with probability one.”
Handbook of Semidefinite Programming (2000, background): “12 can be found in the review paper [127].”
Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices (2007, background): “For instance, a stationary point of (12) is an isolated local minimizer if a second-order sufficient condition holds at that point; see Bonnans and Shapiro (1998). Here we revisit electricity market games, namely the bid-a scenario {(4)}i=1, to show that Nash stationary points are local Nash points ”
Communications and Control for Wireless Drone-Based Antenna Array (2017, methodology): “In general, perturbation theory aims at finding the solution of a complex problem, by starting from the exact solution of a simplified version of the original problem [24].”
Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach (2016, unknown): “erentiability, allowing us to apply the asymptotic results of the previous section. Danskin [24] gave the ﬁrst results on smoothness of the inﬁmum functional (see also the book by Bonnans and Shapiro [15]), and we provide a general statement giving the ﬁrst-order expansion of T(P) as a function of t”
Convex Formulation for Learning from Positive and Unlabeled Data (2015, methodology): “We then derive convergence rates of the empirical estimates and the empirical objectives based on a theory known as perturbation analysis of optimization problems(see Bonnans & Shapiro, 1998; Bonnans & Cominetti, 1996, and references therein).”
Generalized semi-infinite programming: A tutorial (2008, background): “Proposition 5.2 (Bonnans et al. [9], Bannans and Shapiro [ 10 ], Shapiro [78]).”