A Posteriori Error Bounds for the Linearly-Constrained Variational Inequality Problem

By Jong-Shi Pang. 1987

Subfields: Mathematical Optimization, Numerical Methods & Scientific Computing

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Citations in the corpus

A unified approach to error bounds for structured convex optimization problems (2015, methodology): “To demonstrate the power of our proposed framework, we apply it to scenarios (S1)–(S3) and show that the error bound results in [18,27,39,40] can be recovered in a unified manner; see Sects.”
A class of gap functions for variational inequalities (1994, methodology): “[Actually, Patriksson (1991b) shows that [PGG] and (5.”
Distributed Box-Constrained Quadratic Optimization for Dual Linear SVM (2015, unknown): “This local error bound has been shown to hold from the first iteration of the algorithm for both L1- SVM (Pang, 1987, Theorem 3.1) and L2-SVM (Wang & Lin, 2014, Theorem 4.6).”
On the linear convergence of the alternating direction method of multipliers (2012, result): “ion set), deﬁned by dist(y,Y∗) = min y∗∈Y ∗ ky −y∗k, is bounded above by the norm of this residual. Error bounds like this are similar to that in Assumption B and have been studied previously by Pang [41] and by Mangasarian and Shiau [37], though in diﬀerent contexts. The above error bound is ‘local”
Iteration complexity of feasible descent methods for convex optimization (2014, background): “The bound under Assumption 2.1, which requires strong convexity, was already proved in Pang (1987).”
Fixed-Point Continuation for l1-Minimization: Methodology and Convergence (2008, unknown): “Under the first condition, the above result follows from [50] and [41], while under the second condition it follows from [41].”
On the Linear Convergence of the Approximate Proximal Splitting Method for Non-smooth Convex Optimization (2014, background): “For instance, it has been shown that the error bound hold for strongly convex functions in [22], and for quadratic functions with polyhedral constraint in [11, 12].”
Error bounds and convergence analysis of feasible descent methods: a general approach (1993, background): “(See theorem 2.1 for a summary of these results.) In addition, this error bound can be extended to certain linear complementarity problems and variational inequality problems (see [31, 43, 45, 49, 56 ]).”
A projection neural network and its application to constrained optimization problems (2002, methodology): “Different numerical procedures have been presented over decades for solving (1) [1], [2], [6]–[10].”