Cutting planes for low-rank-like concave minimization problems
成果类型：
Article
署名作者：
Porembski, M
署名单位：
Philipps University Marburg
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1040.0151
发表日期：
2004
页码：
942-953
关键词：
摘要：
Concavity cuts play an important role in several algorithms for concave minimization, such as pure cutting plane algorithms, conical algorithms, and branch-and-bound algorithms. For concave quadratic minimization problems Konno et al. (1998) have demonstrated that the lower the rank of the problem, i.e., the smaller the number of nonlinear variables, the deeper the concavity cuts usually turn out to be. In this paper we examine the case where the number of nonlinear variables of a concave minimization problem is large, but most of the objective value of a good solution is determined by a small number of variables only. We will discuss ways to exploit such a situation to derive deep cutting planes. To this end we apply concepts usually applied for efficiently solving low-rank concave minimization problems.