Bi-perspective functions for mixed-integer fractional programs with indicator variables

• 成果类型: Article
• 署名作者: Letchford, Adam N.; Ni, Qiang; Zhong, Zhaoyu
• 署名单位: Lancaster University; Lancaster University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01519-9
• 发表日期: 2021
• 页码: 39-55
• 关键词: power allocation; joint subcarrier; complexity

摘要

Perspective functions have long been used to convert fractional programs into convex programs. More recently, they have been used to form tight relaxations of mixed-integer nonlinear programs with so-called indicator variables. Motivated by a practical application (maximising energy efficiency in an OFDMA system), we consider problems that have a fractional objective and indicator variables simultaneously. To obtain a tight relaxation of such problems, one must consider what we call a bi-perspective (Bi-P) function. An analysis of Bi-P functions leads to the derivation of a new kind of cutting planes, which we call Bi-P-cuts. Computational results indicate that Bi-P-cuts typically close a substantial proportion of the integrality gap.