A preconditioned difference of convex functions algorithm with extrapolation and line search
Ran Zhang, Hongpeng Sun
本文提出了一种新的近端凸差分(DC)算法,通过外推和积极的非莫诺酮线搜索来增强,以解决非凸优化问题。 我们引入了由计算高效的非莫诺酮线搜索确定的外推参数的自适应保守更新策略。 我们算法的核心是将外推参数的更新与非莫诺酮线搜索的步长交互式结合。 两种拟议算法的全球趋同是通过Kurdyka-Łojasiewicz属性建立的,确保了线性方程的先决条件框架内的收敛。 关于两个一般非凸问题的数字实验:SCAD惩罚的二进制分类和基于图形的Ginzburg-Landau图像分割模型,与现有的DC算法相比,在收敛率和解决方案准确性方面证明了该方法的高效率。
This paper proposes a novel proximal difference-of-convex (DC) algorithm enhanced with extrapolation and aggressive non-monotone line search for solving non-convex optimization problems. We introduce an adaptive conservative update strategy of the extrapolation parameter determined by a computationally efficient non-monotone line search. The core of our algorithm is to unite the update of the extrapolation parameter with the step size of the non-monotone line search interactively. The global con...