New Constraint Qualification and Conjugate Duality for Composed Convex Optimization Problems
New Constraint Qualification and Conjugate Duality for Composed Convex Optimization Problems
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DOI：
10.1007/s10957-007-9247-4
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发表时间：
2007-07
影响因子：
1.9
通讯作者：
R. Boț;S. Grad;G. Wanka
中科院分区：
文献类型：
--
作者：
R. Boț;S. Grad;G. Wanka
我们提出了一个新的约束条件，保证强对偶锥约束凸优化问题和它的Fenchel-Lagrange对偶。这个结果被应用到一个凸优化问题，对于一个给定的非空凸锥K，作为目标函数aK-凸函数postcomposed与aK-增加凸函数。对于这个所谓的组合凸优化问题，我们提出了一个强大的对偶断言，太，在较弱的条件下，比迄今为止所考虑的。作为应用，我们重新发现了一个后复合与aK-增凸函数的共轭公式在比文献中通常使用的条件更弱的条件下是有效的。
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 coneK, as objective function aK-convex function postcomposed with aK-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 aK-increasing convex function as valid under weaker conditions than usually used in the literature.