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.

中文翻译：

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具有指示变量的混合整数分数程序的双透视函数

透视函数长期以来一直用于将分数程序转换为凸程序。最近，它们已被用于形成具有所谓指示变量的混合整数非线性程序的紧松弛。受实际应用（在 OFDMA 系统中最大化能源效率）的启发，我们考虑同时具有分数目标和指标变量的问题。为了获得此类问题的严格松弛，必须考虑我们所谓的“双透视”（Bi-P）函数。对 Bi-P 函数的分析导致推导出一种新的切割平面，我们称之为“Bi-P-cuts”。计算结果表明 Bi-P-cuts 通常会关闭很大一部分的完整性差距。