Asymptotic cones and functions in optimization and variational inequalities

By Alfred Auslender, Marc Teboulle. 2002

456 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/b4e939143c6baeb86ba54397c807cbfa913c200d

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In Computational Theory and Mathematics

Citations in the corpus

A Primer on Monotone Operator Methods (2015, background): “Standard references on convex optimization and convex analysis (which contain far more than the reader needs) include [111, 4, 16, 20, 94, 17, 120, 14, 18, 13, 15].”
Firmly Nonexpansive Mappings and Maximally Monotone Operators: Correspondence and Duality (2011, unknown): “Suppose that T = JA, that N = 2T − Id, and that β ∈ [0, 1].”
Characterizations of error bounds for lower semicontinuous functions on metric spaces (2004, background): “is contained in the relative interior of domf , an equivalent formulation of the first assertion in Proposition 3.2 can be found in [ 3 ] (Prop.”
Hybrid methods with regularization for minimization problems and asymptotically strict pseudocontractive mappings in the intermediate sense (2009, background): “For further details on variational inequalities, we refer to [8–13] and the references therein.”
A survey on error bounds for lower semicontinuous functions (2003, background): “This is proved in [4] in finite dimension under an assumption on the relative interior of the domain of f which is removed here.”
Convex Functions: Constructions, Characterizations and Counterexamples (2010, background): “Again, it is relatively easy to relativize this result to the intrinsic core; this is especially useful in finite dimensions, see [24].”
Smoothing and First Order Methods: A Unified Framework (2012, methodology): “Some earlier works on the subject can be found, for example, in [16, 11, 12, 10], and for a more recent account, see, for instance, [3] and references therein.”
A new class of costs for optimal transport planning (2018, unknown): “4 in [2]): (G∗)∞(x,ψ) = lim t→+∞ G∗(x, tψ) t = sup {∫”
New Farkas-type constraint qualifications in convex infinite programming (2007, background): “Su¢ cient conditions for the inf-stability in other context (non-convex objective function and linear equality constraints) are given in [1].”
Stability for convex vector optimization problems (2004, background): “9 in [3] that A \ f yþe is a bounded set.”