New Constraint Qualification and Conjugate Duality for Composed Convex Optimization Problems

R. I. Boţ, S. M. Grad and G. Wanka ()
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R. I. Boţ: Chemnitz University of Technology
S. M. Grad: Chemnitz University of Technology
G. Wanka: Chemnitz University of Technology

Journal of Optimization Theory and Applications, 2007, vol. 135, issue 2, No 4, 255 pages

Abstract: Abstract We present a new constraint qualification which guarantees strong duality between a cone-constrained convex optimization problem and its Fenchel-Lagrange dual. This result is applied to a convex optimization problem having, for a given nonempty convex cone K, as objective function a K-convex function postcomposed with a K-increasing convex function. For this so-called 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 K-increasing convex function as valid under weaker conditions than usually used in the literature.

Keywords: Conjugate functions; Fenchel-Lagrange duality; Composed convex optimization problems; Cone constraint qualifications (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-007-9247-4

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