两类解非线性约束问题的超记忆可行方向法

Two Classes of Supermemory Feasible Direction Methods for Solving Nonlinear Inequality Constrained Optimization

本文将无约束超记忆梯度法推广到非线性不等式约束优化问题上来,给出了两类形式很一般的超记忆可行方向法,并在非退化及连续可微等较弱的假设下证明了其全局收敛性.适当选取算法中的参量及记忆方向,不仅可得到一些已知的方法及新方法,而且还可能加快算法的收敛速度.

This paper extends the supermemory gradient methods for unconstrained optimization to nonlinear inequality consirained optimization and presents two classes of supermemory feasible direction methods with general forms. Under the assumptions of nondegeneracy and continuous differentiability, any algorithm in these ciasses is globally convergent. When selecting proper parameters and memory directions in the methods, some known methods and new methods are obtained, and the rate of convergence of the methods may be increased.