Error bounds in mathematical programming

By Jong-Shi Pang. 1997

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In Mathematical Optimization

Citations in the corpus

Frank-Wolfe Splitting via Augmented Lagrangian Method (2018, background): “The optimization literature named such properties error bounds (Pang, 1997).”
A Conditional Gradient-based Method for Simple Bilevel Optimization with Convex Lower-level Problem (2022, background): “We note that the error bound condition in (11) is well-studied in the optimization literature (see (Pang, 1997; Bolte et al., 2017; Roulet and d’Aspremont, 2020) and the references therein) and is known to hold generally when the function g is analytic and the set Z is bounded (Łojasiewicz, 1959;…”
From error bounds to the complexity of first-order descent methods for convex functions (2015, background): “The survey of Pang [56] provides a comprehensive panorama of results obtained around this time.”
A unified approach to error bounds for structured convex optimization problems (2015, background): “…from Before we proceed further, let us brieﬂy illustrate some of the concepts above. and there exist constants κ, ǫ > 0 such that The notions of calmness and metric sub-regularity have played a central role in the study of error bounds; see, e.g. , [26, 9, 31, 27, 15] and the references therein.”
Exact penalty results for mathematical programs with vanishing constraints (2010, background): “In the first result, we see that calmness of the perturbation map at a particular point is in fact equivalent to the existence of local error bounds, see [18].”
Bounded Linear Regularity, Strong CHIP, and CHIP are Distinct Properties (2000, background): “These geometric properties are key in the study of various areas in convex optimization and bordering fields, such as: Fenchel duality [13, 12]; duality for convex cones [19]; systems of convex inequalities and associated error bounds [22, 23, 9]; projection algorithms and their rate of convergence ”
Golden ratio algorithms for variational inequalities (2018, methodology): “For a survey of error bounds, we refer the reader to [46] and for their applications to the VI algorithms to [50,56].”
Randomized Methods for Linear Constraints: Convergence Rates and Conditioning (2008, unknown): “A comprehensive survey of error bounds for a variety of problems arising in optimization can be found in Pang [35].”
New fractional error bounds for polynomial systems with applications to Hölderian stability in optimization and spectral theory of tensors (2015, background): “We also refer the reader to [6,7,22,23,25,30,48,49,58] and the bibliographies therein for other approaches to error bounds and their numerous applications.”
Some recent advances in projection-type methods for variational inequalities (2003, background): “An excellent survey of research in this area prior to 1990 can be found in Harker and Pang [36].”
Trust-region quadratic methods for nonlinear systems of mixed equalities and inequalities (2009, unknown): “6) is assumed to hold in a region of the form Bρ(x∗) ∩ Ω [30].”
Some Exact Penalty Results for Nonlinear Programs and Mathematical Programs with Equilibrium Constraints (2003, background): “(b) Let x̄∈X be a solution of problem (7).”
Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers (2020, background): “Despite a vast amount of work [15, 2] and experimental evaluations [7, 41], analytic descriptions of these errors remain elusive for most real-world applications of simulations.”
Error bounds and metric subregularity (2014, methodology): “The interested reader is referred to the articles by Azé [1], Azé and Corvellec [2], Corvellec and Motreanu [3], Gfrerer [4], Ioffe [5], Ioffe and Outrata [6], Ngai and Théra [7,8], Jong-Shi Pang [9], Zheng and Ng [10,11] and the references therein.”