Estimates of the Duality Gap in Nonconvex Optimization
Estimates of the Duality Gap in Nonconvex Optimization
复制标题
非凸优化中对偶间隙的估计
DOI：
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发表时间：
1976
影响因子：
1.7
通讯作者：
I. Ekeland
中科院分区：
文献类型：
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作者：
J. Aubin;I. Ekeland
我们将每一个实值函数与一个度量其凸性缺乏的数联系起来。这个数字是用来估计的对偶间隙在优化问题的标准和/或约束是非凸的。它表明，当变量的数量是非常大的约束的数量，这个对偶差距是相对值小。以这种方式近似的标准和约束作为积分的问题，我们表明，对偶间隙消失。
We associate with every real-valued function a number which measures its lack of convexity. This number is used to estimate the duality gap in optimization problems where the criterion and/or the constraints are nonconvex. It is shown that when the number of variables is very great with respect to the number of constraints, this duality gap is small in relative value. Approximating in this way problems where the criterion and constraints are given as integrals, we show that the duality gap vanishes.