On the generalization of ECP and OA methods to nonsmooth convex MINLP problems
On the generalization of ECP and OA methods to nonsmooth convex MINLP problems
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DOI：
10.1080/02331934.2012.712118
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发表时间：
2014-06
期刊：
影响因子：
2.2
通讯作者：
V. Eronen;M. Mäkelä;T. Westerlund
中科院分区：
文献类型：
--
作者：
V. Eronen;M. Mäkelä;T. Westerlund
本文研究了一些混合整数非线性规划算法在凸非光滑问题上的推广。在扩展割平面法中，梯度被凸函数的次梯度所代替，由此产生的算法应被证明收敛于全局最优。它示出通过一个反例，这种类型的泛化是不够的，某些版本的外部近似算法。然而，与一些修改的外逼近方法的一种特殊类型的非光滑函数，其中的次微分在任何一点是一个凸组合的有限数量的次梯度在该点可以考虑。文中还报道了用扩展割平面法进行数值计算的结果。
In this article, generalization of some mixed-integer nonlinear programming algorithms to cover convex nonsmooth problems is studied. In the extended cutting plane method, gradients are replaced by the subgradients of the convex function and the resulting algorithm shall be proved to converge to a global optimum. It is shown through a counterexample that this type of generalization is insufficient with certain versions of the outer approximation algorithm. However, with some modifications to the outer approximation method a special type of nonsmooth functions for which the subdifferential at any point is a convex combination of a finite number of subgradients at the point can be considered. Numerical results with extended cutting plane method are also reported.