Truncated aggregate homotopy method for nonconvex nonlinear programming
Truncated aggregate homotopy method for nonconvex nonlinear programming
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DOI：
10.1080/10556788.2012.762365
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发表时间：
2014-01
影响因子：
2.2
通讯作者：
Y. Xiao;H. Xiong;Bo Yu
中科院分区：
文献类型：
--
作者：
Y. Xiao;H. Xiong;Bo Yu
提出了一种求解非凸非线性规划问题的聚同伦方法的有效实现。采用截断聚合技术，每次迭代只聚合一小部分约束，从而大大减少了梯度和Hessian计算的次数。利用一些可实现的截断准则自适应地更新子集，以尽可能少的计算代价保证修正过程的局部二次收敛。数值试验与其他方法的比较表明，新方法是非常有效的，特别是对于具有大量约束和{计算昂贵}梯度或Hessians的问题。
In this paper, an efficient implementation of aggregate homotopy method for nonconvex nonlinear programming problems is proposed. Adopting truncated aggregate technique, only a small subset of the constraints is aggregated at each iteration, hence the number of gradient and Hessian calculations is reduced dramatically. The subset is adaptively updated with some cheaply implementable truncating criterions, to guarantee the locally quadratic convergence of the correction process with as few computation cost as possible. Numerical tests with comparison to some other methods show that the new method is very efficient, especially for the problems with large amount of constraints and {computationally expensive} gradients or Hessians.