一种解无约束优化问题的新移动渐近线算法

A New Algorithm of Moving Asymptotes for Solving Unconstrained Optimization Problems

对无约束优化问题,本文提出了一种新的移动渐近线算法.在每次迭代过程中,我们构造一个原问题的移动渐近线函数,由此建立一个简单可分、严格凸的子问题,通过求解子问题获得下降搜索方向,再用线搜索取得搜索步长.文中讨论了算法的参数取值原则,并证明了算法的全局收敛性.数值试验结果表明算法是有效的、适合解大规模的无约束优化问题.

This paper aims to introduce a new algorithm of moving asymptotes for unconstrained optimization problems. The principle of the proposed algorithm is to construct a moving asymptotes function in each iteration. Based on this construction, the original problem can be transformed into a simple, separable and strictly convex sub-problem. We obtain the descending direction by solving this sub-problem and carry out the search step by virtue of the line search technique. The concrete selection of the parameters is examined. Further, we prove that the algorithm is global convergent. The numerical results show that the algorithm is effective and can be used to deal with some large-scale unconstrained optimization problems.