一种有效的求解无约束优化问题的共轭方向法

§1.前言 有些实践中的优化问题可以按无约束来处理,而且大量非常有效的约束优化算法都涉及无约束优化方法,因此,无约束优化方法在实用上是很重要的。 考虑下面的二次目标函数F(X)的无约束优化问题:

AN EFFICIENT CONJUGATE DIRECTION METHOD FOR UNCONSTRAINED FUNCTION MINIMIZATION

Based on the properties of conjugate vecrors, a new algorithm for unconstrained functionminimization is developed. The algorithm belongs to the direct search method and is ? conju-gate direction-type method with the property of quadratic termination. Compared with som pre-viouly developed direct search methods including the convensional modified Powell method,the number of one-dimensional search is reduced to the minimum, i.e. only one search in aniterating cycle. In addition, the algorithm presented is simple in calculation and easy incoding, and has the capability of accelerating along the "ridges". The method is compared with three direct search metheds including the modifiedPowell method on many test problems. Numerical results show the efficiency and robustness ofthe new algorithm.