Biperspective functions for mixed-integer fractional programs with indicator variables

Letchford, Adam and Ni, Qiang and Zhong, Zhaoyu (2021) Biperspective functions for mixed-integer fractional programs with indicator variables. Mathematical Programming, 190 (1-2). pp. 39-55. ISSN 0025-5610

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Abstract

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.