二次罚函数的可分化方法

Decomposition Methods in Quadratic Penalty Function

可分方法用于将一个复杂的大规模优化问题分解成各个子问题进行求解。本文对可分优化问题给出两种可分方法,即分别将辅助问题原理(APP)方法和分块协调下降(BCD)方法应用于二次罚函数方法(QPM),并提出相应的QPM+APP算法和QPM+BCD算法,使得在求解可分优化问题时仅需要修正罚因子。最后给出了两个算例,通过与文献[1]中的ALR+APP和ALR+BCD算法作比较来求解,所得的计算结果说明本文给出的两种算法是具有有效性的。

The decomposition methods are used to solve large-scale optimization problems by decomposing them into sub-problems. In this paper we present two decomposition methods for solving separable optimization problems. We apply the Auxiliary Problem Principle （APP） method and the Block Coordinate Descent （BCD） method to the Quadratic Penalty Method （QPM） respectively and also present the corresponding QPM ＋ APP Algorithm and QPM ＋ BCD Algorithm. Meanwhile, In Ref. 1, for a separable problem the authors apply the APP and BCD method to the Augmented Lagrangian Relaxation （ALR）method and solve the problem, so both the dual variable and the penalty parameter must be updated. But we only update the penalty parameter by the present methods. Two numerical examples are given to show the usefulness of the presented methods by comparing with the ALR ＋ BCD and the ALR ＋ BCD Algorithm in Ref. 1.