一种求解非线性优化问题的可行方向法

针对目前常用的解线性约束的非线性优化问题的方法在实际应用中还存在不收敛、收敛较慢,或"基变量大量达界后,找不到新的入基变量"等问题,该文提出了求解该问题的新方法夹逼可行方向法,已证明算法的最优性与收敛性。指出夹逼可行方向法可视为Frank-Wolfe算法的推广,也可视为是Zoutendijk可行方向法和逐次线性近似方法的改进算法。算例表明,算法收敛速度较Zoutendijk可行方向法、Frank-Wolfe方法等有了较大提高。算法已被研制成实用软件,并成功应用于三峡电力系统优化调度和调峰方式研究中。

Feasible direction algorithm for solving nonlinear optimization problems

This paper introduces the approaching feasible direction algorithm (AFDA) for solving linearly constrained nonlinear programming problems. The optimality and convergence of the AFDA has been proved. The AFDA can be regarded as a generalizationof the Frank-Wolfe feasible direction algorithm and an improvement of the Zoutendijk feasible direction algorithm and the successive linear approximation algorithm. The algorithm was implemented in a practical software package that has been applied to optimal scheduling and peak load following problems in the Three Gorges power system. The results show that the algorithm is fast and effective.