Bibliographic Details
| Title: |
New Constraint Qualification and Conjugate Duality for Composed Convex Optimization Problems. |
| Authors: |
Boƫ, R. I.1, Grad, S. M.1, Wanka, G.1 gert.wanka@mathematik.tu-chemnitz.de |
| Source: |
Journal of Optimization Theory & Applications. Nov2007, Vol. 135 Issue 2, p241-255. 15p. |
| Subjects: |
Mathematical optimization, Convex functions, Real variables, Conjugate direction methods, Numerical solutions to equations, Mathematics, Mathematical analysis, Numerical analysis, Mathematical variables |
| 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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
