一种新的自适应步长梯度投影法

A NEW GRADIENT PROJECTION METHOD WITH SELF-ADAPTIVE STEP SIZE

梯度投影法是一种求解约束优化问题的经典算法.它具有单步计算量低等优点,但其效率受步长规则影响较大.本文提出的一种新的自适应步长规则的梯度投影法.该算法一方面,它无需函数值信息;另一方面,它的步长接受规则比Armijo规则更为宽松,因而可以接受较长的步长以加速收敛.初步的数值实验表面新算法较为高效.

Gradient Projection method is a classic algorithm for solving constrained optimization. It takes the advantage of its low per-iteration cost. However, its efficiency can be affected by the choice of step size. In this paper, we propose a new Gradient Projection method with self-adaptive step size rule. On the hand, it does not need the information of objective; on the other hand, it can accept longer step size than that based on Armijo rule to accelerate the convergence. Our preliminary experimental results show that it is an efficient algorithm.