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A new constraint qualification for the formula of the subdifferential of composed convex . . .
, 2005
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A new constraint qualification and conjugate duality for composed convex optimization problems
 J. Optimization Theory Appl
, 2004
"... Abstract We present a new constraint qualification which guarantees strong duality between a coneconstrained convex optimization problem and its FenchelLagrange dual. This result is applied to a convex optimization problem having, for a given nonempty convex cone K, as objective function a Kconve ..."
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Cited by 7 (4 self)
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Abstract We present a new constraint qualification which guarantees strong duality between a coneconstrained convex optimization problem and its FenchelLagrange dual. This result is applied to a convex optimization problem having, for a given nonempty convex cone K, as objective function a Kconvex function postcomposed with a Kincreasing convex function. For this socalled composed convex optimization problem, we present a strong duality assertion, too, under weaker conditions than the ones considered so far. As an application, we rediscover the formula of the conjugate of a postcomposition with a Kincreasing convex function as valid under weaker conditions than usually used in the literature. Keywords Conjugate functions · FenchelLagrange duality · Composed convex optimization problems · Cone constraint qualifications
Revisiting Some Duality Theorems via the Quasirelative Interior in Convex Optimization
"... In this paper we deal with regularity conditions, formulated by making use of the quasirelative interior and/or of the quasi interior of the sets involved, which guarantee strong duality for a convex optimization problem with cone (and equality) constraints and its Lagrange dual. We discuss also s ..."
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Cited by 5 (3 self)
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In this paper we deal with regularity conditions, formulated by making use of the quasirelative interior and/or of the quasi interior of the sets involved, which guarantee strong duality for a convex optimization problem with cone (and equality) constraints and its Lagrange dual. We discuss also some results recently on this topic, which are proved to have either superfluous or contradictory assumptions. Several examples illustrate the theoretical considerations.
New regularity conditions for Lagrange and FenchelLagrange duality in infinite dimensional spaces
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CONSTRAINT QUALIFICATIONS FOR EXTENDED FARKAS’S LEMMAS AND LAGRANGIAN DUALITIES IN CONVEX INFINITE PROGRAMMING
"... Abstract. For an inequality system defined by a possibly infinite family of proper functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions. Under the new constraint qualifications, we ..."
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Cited by 4 (1 self)
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Abstract. For an inequality system defined by a possibly infinite family of proper functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions. Under the new constraint qualifications, we obtain characterizations of those reverseconvex inequalities which are consequence of the constrained system, and we provide necessary and/or sufficient conditions for a stable Farkas lemma to hold. Similarly, we provide characterizations for constrained minimization problems to have the strong or strong stable Lagrangian dualities. Several known results in the conic programming problem are extended and improved. Key words. convex inequality system, Farkas lemma, strong Lagrangian duality, conic programming
Farkastype results and duality for DC programs with convex constraints
 J. Convex Anal
"... convex constraints ..."
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Regularity conditions for formulae of biconjugate functions, submitted
"... Abstract. When the dual of a normed space X is endowed with the weak ∗ topology, the biconjugates of the proper convex lower semicontinuous functions defined on X coincide with the functions themselves. This is not the case when X ∗ is endowed with the strong topology. Working in the latter framewor ..."
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Cited by 1 (1 self)
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Abstract. When the dual of a normed space X is endowed with the weak ∗ topology, the biconjugates of the proper convex lower semicontinuous functions defined on X coincide with the functions themselves. This is not the case when X ∗ is endowed with the strong topology. Working in the latter framework, we give formulae for the biconjugates of some functions that appear often in convex optimization, which hold provided the validity of some suitable regularity conditions. We also treat some special cases, rediscovering and improving recent results in the literature. Finally, we give a regularity condition that guarantees that the biconjugate of the supremum of a possibly infinite family of proper convex lower semicontinuous functions defined on a separated locally convex space coincides with the supremum of their biconjugates. 1.
unknown title
, 2009
"... Regularity conditions via generalized interiority notions in convex optimization: new achievements and their relation to some classical statements ..."
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Regularity conditions via generalized interiority notions in convex optimization: new achievements and their relation to some classical statements