A Comparison of Constraint Qualifications in Infinite-Dimensional Convex Programming

Gowda, M. Seetharama; Teboulle, Marc

doi:10.1137/0328051

Cited by 63 publications

(45 citation statements)

References 8 publications

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“…As shown by Gowda and Teboulle (1990) and Zȃlinescu (1999), the strong quasirelative interior condition (16) and our condition (14) based on the intrinsic core are related to each other by the following equivalence:…”

Section: (Bl)mentioning

confidence: 99%

“…Thus, our constraint qualification condition (14) is strictly weaker than that of Gowda and Teboulle (1990) in (16) (which we recall again is the generalization of the constraint qualification condition by Borwein and Lewis (1993) that works for problems with conditional moment restrictions). Specifically, our condition (14) does not involve any closedness requirements.…”

Section: (Bl)mentioning

confidence: 99%

“…For this, we need a generalized version of Borwein and Lewis's (1993) quasi-relative interior condition, which works for linear mappings that map into general Banach spaces. Gowda and Teboulle (1990) propose one such generalized condition, based on the notion of a strong quasi-relative interior, whereby sqri(A) ≡ {a ∈ A : cone(A − a)is a closed subspace}. Their condition can be written as:…”

Section: (Bl)mentioning

confidence: 99%

“…There is a variety of constraint qualification conditions that have been proposed in the literature (see, e.g., Gowda and Teboulle, 1990;Zȃlinescu, 1999, for reviews). In this paper, we shall work with the following constraint qualification proposed by Zȃlinescu (1999) (Theorem 8(v)):…”

Section: Strong Dualitymentioning

confidence: 99%

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Existence and Characterization of Conditional Density Projections

Komunjer

Ragusa

2015

Econom. Theory

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In this paper we propose primitive conditions under which a projection of a conditional density onto a set defined by conditional moment restrictions exists and is unique. Moreover, we provide an analytic expression of the obtained projection. The range of applications where conditional density projections are used is wide. The derived results are potentially useful in a variety of areas including: semiparametric efficient estimation and optimal testing in (conditional) moment models, Bayesian prior determination and inference in semiparametric models, density forecasting, and simulation-based econometric analysis.Regarding existence, we propose three different combinations of assumptions that are all sufficient to show that the projection exists and is unique. The proposed conditions exhibit a clear trade off between restrictions put on the divergence between the conditional densities and on the moment function which defines the projection set. Depending on the nature of the application, the researcher can pick and choose which set of conditions to use. Our second set of results characterizes the projection. The expression for the projected density is new though not surprising given the previously obtained results for the unconditional case. The projection is characterized by the dual of the original projection problem. In establishing the strong duality, however, we work with a constraint qualification condition that is weaker than that used by Borwein and Lewis (1991a, 1992a in their seminal work concerning the unconditional case.

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Section: (Bl)mentioning

confidence: 99%

Section: (Bl)mentioning

confidence: 99%

Section: (Bl)mentioning

confidence: 99%

Section: Strong Dualitymentioning

confidence: 99%

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Existence and Characterization of Conditional Density Projections

Komunjer

Ragusa

2015

Econom. Theory

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“…If the interior-point condition that (int D) ∩ C = ∅ (or its recent generalization that the cone generated by (C − D), cone(C − D), is a closed subspace [13,15,10]) is satisfied or the bounded linear regularity condition [4,5], when X is a Euclidean space, is satisfied, then the normal cone intersection formula …”

Section: Introductionmentioning

confidence: 99%

A simple closure condition for the normal cone intersection formula

Burachik¹,

Jeyakumar

2004

Proc. Amer. Math. Soc.

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A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces

Boţ

Grad

Wanka

2008

Mathematische Nachrichten

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In this paper we work in separated locally convex spaces where we give equivalent statements for the formulae of the conjugate function of the sum of a convex lower-semicontinuous function and the precomposition of another convex lower-semicontinuous function which is also K-increasing with a K-convex K-epi-closed function, where K is a nonempty closed convex cone. These statements prove to be the weakest constraint qualifications given so far under which the formulae for the subdifferential of the mentioned sum of functions are valid. Then we deliver constraint qualifications inspired from them that guarantee some conjugate duality assertions. Two interesting special cases taken from the literature conclude the paper.

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A Comparison of Constraint Qualifications in Infinite-Dimensional Convex Programming

Cited by 63 publications

References 8 publications

Existence and Characterization of Conditional Density Projections

Existence and Characterization of Conditional Density Projections

A simple closure condition for the normal cone intersection formula

A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces

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