A FAMILY OF SEARCH DIRECTIONS FOR KARMARKARS ALGORITHM
成果类型：
Article
署名作者：
ANSTREICHER, KM; WATTEYNE, P
署名单位：
Universite Catholique Louvain
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.41.4.759
发表日期：
1993
页码：
759-767
关键词：
摘要：
We consider a new family of search directions for the standard form variant of Karmarkar's projective linear programming algorithm. The family includes the usual projected gradient direction, and also a direction first proposed by Mike Todd. We prove that any choice from the family preserves the algorithm's polynomial-time complexity. We then examine the computational behavior of the algorithm using different choices of directions. Although the theoretical complexity is the same for the different directions, in practice we find wide variations in algorithm performance. One particular choice consistently requires about 20% fewer iterations than the usual direction, while another requires a number of iterations which grows rapidly with problem size. Our computational results also demonstrate that a small number of monotonic steps on early iterations may considerably improve the performance of the algorithm.