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New Constraint Qualification and Conjugate Duality for Composed Convex Optimization Problems

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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.

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Authors and Affiliations

  1. Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany

    R. I. Boţ, S. M. Grad & G. Wanka

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  1. R. I. Boţ
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  2. S. M. Grad
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  3. G. Wanka
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Correspondence to G. Wanka.

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Communicated by T. Rapcsák.

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Boţ, R.I., Grad, S.M. & Wanka, G. New Constraint Qualification and Conjugate Duality for Composed Convex Optimization Problems. J Optim Theory Appl 135, 241–255 (2007). https://doi.org/10.1007/s10957-007-9247-4

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