【摘要】 拟牛顿算法是无约束优化问题的一类重要算法。它不但计算效率高,数值效果稳定,而且对其适当修正后可用于求解约束优化问题。但拟牛顿算法的校正公式种类繁多,结构复杂,收敛性证明繁琐,这使得很多运筹学专业研究生在学习这部分内容时望而却步,同时也使很多主讲教师在讲授这部分内容时,不能保证教学效果。对此,我们基于无约束优化问题的拟牛顿条件,以校正项为线索逐步引出拟牛顿算法的秩校正公式和秩校正公式,并对它们之间的关系进行探讨,以期给拟牛顿算法的诸多校正公式一个清晰的逻辑结构,提高《最优化方法》课程的教学效果。更多还原

【Abstract】 Quasi Newton algorithm is an important algorithm for unconstrained optimization problems.It not only has high efficiency and stable numerical effect,but also can be used to solve constrained optimization problems after appropriate modification.However,there are many kinds of updated formulas of quasi Newton algorithm,and they have complicated structures and tedious proof of convergence,which makes many graduate students of operational research major flinch from learning this part of content,and also makes many lecturers have no idea about the teaching effect when they teach this part of content.To solve the problem,based on the quasi Newton condition,the rank-1 updated formula and some rank-2 updated formulas of quasi Newton algorithm are derived step by step with the correction term as the clue,and the relationship between them is discussed in order to provide a clear logical structure for many correction formulas of quasi Newton algorithm> We hope this can help improve the teaching effect of optimization method course.更多还原