TY - JOUR

T1 - Biperspective functions for mixed-integer fractional programs with indicator variables

AU - Letchford, Adam

AU - Ni, Qiang

AU - Zhong, Zhaoyu

PY - 2021/11/30

Y1 - 2021/11/30

N2 - 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.

AB - 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.

KW - mixed-integer nonlinear programming

KW - mobile wireless communications

KW - OFDMA systems

U2 - 10.1007/s10107-020-01519-9

DO - 10.1007/s10107-020-01519-9

M3 - Journal article

VL - 190

SP - 39

EP - 55

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1-2

ER -