Minimizing Lipschitz-continuous strongly convex functions over integer points in polytopes
Minimizing Lipschitz-continuous strongly convex functions over integer points in polytopes
复制标题
最小化多面体整数点上的 Lipschitz 连续强凸函数
DOI：
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复制
发表时间：
2012
影响因子：
2.7
通讯作者：
R. Weismantel
中科院分区：
文献类型：
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作者：
M. Baes;Alberto Del Pia;Y. Nesterov;S. Onn;R. Weismantel
本文是关于多面体整数点上 Lipschitz 连续强凸函数的最小化。我们的结果与黑盒算法的收敛速度有关，该算法以恒定的近似因子迭代解决特殊的二次整数问题。尽管潜在问题具有普遍性，但我们证明，根据我们对问题编码的假设，我们可以有效地找到目标函数值接近最优值的可行解决方案。我们还表明，在问题的编码长度的因子多项式范围内，这种接近结果是最好的。
This paper is about the minimization of Lipschitz-continuous and strongly convex functions over integer points in polytopes. Our results are related to the rate of convergence of a black-box algorithm that iteratively solves special quadratic integer problems with a constant approximation factor. Despite the generality of the underlying problem, we prove that we can find efficiently, with respect to our assumptions regarding the encoding of the problem, a feasible solution whose objective function value is close to the optimal value. We also show that this proximity result is the best possible up to a factor polynomial in the encoding length of the problem.
DOI：
10.1137/070696465
发表时间：
2008
期刊：
ArXiv
影响因子：
--
作者：
Y. Berstein;S. Onn;H. Maruri;H. Wynn;E. Riccomagno;R. Weismantel
通讯作者：
R. Weismantel