The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems
The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems
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DOI：
10.1007/s10479-004-5022-1
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发表时间：
2005-01-01
影响因子：
4.8
通讯作者：
Tao, PD
中科院分区：
文献类型：
--
作者：
An, LTH;Tao, PD
DC规划及其DC算法（DCA）研究函数f = g-h（g为Rn上的下连续真凸函数）在全空间上的极小化问题。基于局部最优性条件和DC对偶，DCA被成功地应用于许多不同的和各种各样的不可微非凸优化问题，它经常给出全局解，并被证明比相关的标准方法更鲁棒和更有效，特别是在大规模的设置。DCA的计算效率建议我们对DC规划进行更深入和更完整的研究，使用特殊的DC规划类（当g或h是多面体凸的）称为多面体DC规划。DC对偶的研究方法简单，便于最优性条件的研究。给出了局部最优性的新的实用结果。我们强调DC规划中的正则化技术，以构造合适的等价DC规划来解决不可微非凸优化问题和新的重要问题。对DCA进行了更深入的分析，这对DCA有了新的认识，并可以部分解释其效率。最后给出了真实的世界非凸优化问题的DC模型。
The DC programming and its DC algorithm (DCA) address the problem of minimizing a function f = g - h (with g, It being lower semicontinuous proper convex functions on R-n) on the whole space. Based on local optimality conditions and DC duality, DCA was successfully applied to a lot of different and various nondifferentiable nonconvex optimization problems to which it quite often gave global solutions and proved to be more robust and more efficient than related standard methods, especially in the large scale setting. The computational efficiency of DCA suggests to us a deeper and more complete study on DC programming, using the special class of DC programs (when either g or h is polyhedral convex) called polyhedral DC programs. The DC duality is investigated in an easier way, which is more convenient to the study of optimality conditions. New practical results on local optimality are presented. We emphasize regularization techniques in DC programming in order to construct suitable equivalent DC programs to nondifferentiable nonconvex optimization problems and new significant questions which have to be answered. A deeper insight into DCA is introduced which really sheds new light on DCA and could partly explain its efficiency. Finally DC models of real world nonconvex optimization are reported.