A comparison of constraint quali cations in in nite-dimensional convex programming

By M. Seethharama Gowda, Marc Teboulle. 1990

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In Optimization & Training

Citations in the corpus

Frank-Wolfe Splitting via Augmented Lagrangian Method (2018, background): “It is a particular case of constraint qualiﬁcations (Holmes, 1975; Gowda and Teboulle, 1990).”
An alternative formulation for a new closed cone constraint qualification (2006, unknown): “[8]): (SCQ) ⇒ (RCQ) ⇒ (JWCQ) ⇔ (GTCQ).”
Regularity conditions via generalized interiority notions in convex optimization: New achievements and their relation to some classical statements (2009, background): “[13], see also [25] and [47, Theorem 2.”
A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces (2006, background): “Among the large number of works which deal with this subject we want to mention [14], [17], [18], [20], [21], [23], [24], where different so-called generalized interior-point regularity conditions have been introduced.”
A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces (2008, background): “We do not mention all of them here, though we refer the reader to [9] and [15] (Theorem 2.”
Notions of Relative Interior in Banach Spaces (2003, background): “Rockafellar [16] proposed a constraint qualification in terms of the core of a convex set; we state a slight refinement of that result below (for the proof, see [ 10 ]; this reference, as well as [12], contains a discussion of various constraint qualifications in several special cases).”
AN OLD‐NEW CONCEPT OF CONVEX RISK MEASURES: THE OPTIMIZED CERTAINTY EQUIVALENT (2007, background): “For that, by invoking general convex duality results (see, e.g., Borwein and Lewis 1992, Corollary 4.8, p. 35; Gowda and Teboulle 1990, theorem 3.4, p. 929), one needs to verify that the following constraint qualification holds: (CQ) ∃ẑ ∈ L1 such that ∫ ẑ(ω)dP(ω) = 1, α < ẑ(ω) < β a.e.”
Revisiting Some Duality Theorems via the Quasirelative Interior in Convex Optimization (2008, unknown): “The relations (1) and (2) give us 〈x∗, a′ − a′′〉 ≤ 0, ∀a′, a′′ ∈ A, so x∗ ∈ NA−A(OX).”