The Validity of a Family of Optimization Methods
The Validity of a Family of Optimization Methods
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DOI：
10.1137/0308003
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发表时间：
1970-02
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影响因子：
--
通讯作者：
R. Meyer
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文献类型：
--
作者：
R. Meyer
本文描述了一类迭代优化方法，并分析了其聚点的性质。结果表明，这些聚点具有理想的性质，在适当的假设下，对相关的点集映射。这些假设的条件下举行，然后讨论了一些算法，包括最速下降法，弗兰克-沃尔夫方法，可行方向法，和一些二阶方法。五个算法的一类特殊的非凸问题也以同样的方式进行了分析。最后，它示出的结果可以扩展到的情况下，其中所构造的子问题仅近似解决和算法是两个或两个以上的算法的复合材料。
A family of iterative optimization methods, which includes most of the well-known algorithms of mathematical programming, is described and analyzed with respect to the properties of its accumulation points. It is shown that these accumulation points have desirable properties under appropriate assumptions on a relevant point-to-set mapping. The conditions under which these assumptions hold are then discussed for a number of algorithms, including steepest descent, the Frank–Wolfe method, feasible direction methods, and some second order methods. Five algorithms for a special class of nonconvex problems are also analyzed in the same manner. Finally, it is shown that the results can be extended to the case in which the subproblems constructed are only approximately solved and to algorithms which are composites of two or more algorithms.