Perturbation Analysis of Optimization Problems

By J. Bonnans, Alexander Shapiro. Springer Series in Operations Research, 2000

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Conditional Risk Mappings (2006, methodology): “In our earlier work [17] we have refined and extended the analysis of [1, 6, 5, 7, 15].”
On Uniform Convexity, Total Convexity and Convergence of the Proximal Point and Outer Bregman Projection Algorithms in Banach Spaces (2003, neutral): “Recall (see, for instance, [8]) that g∗ = f and, therefore, f ′ = g∗′ = (g′)−1.”
Second-Order Optimality Conditions in Set Optimization (2005, positive): “Remark 3.2. It is evident that ( 6 ) and (5) hold as first-order and second-order necessary optimality conditions if Dc(F + CY )( ¯ x, ¯ y) is replaced by Dg F( ¯ x, ¯ y) or DF ( ¯ x, ¯ y) and if D 2 (F + CY )( ¯ x, ¯ y, ¯ u, ¯ v) is replaced by D 2 g F( ¯ x, ¯ y, ¯ u, ¯ or D 2 F( ¯ x, ¯ y, ¯ u, ¯ v”
An augmented Lagrangian dual approach for the H-weighted nearest correlation matrix problem (2011, background): “For the origin of the constraint nondegeneracy, its various forms, and its role in general optimization, see [6, 7 , 25, 26, 27, 33].”
Empirical optimal transport on countable metric spaces: Distributional limits and statistical applications (2017, methodology): “We will use Theorem 4.24 from Bonnans and Shapiro (2000).”