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A logarithmic method for eliminating binary variables and constraints for the product of free-sign discrete functions

机译：消除自由变量离散函数乘积的二进制变量和约束的对数方法

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In this paper, a logarithmic method was developed to solve optimization problems containing the product of free-sign discrete functions (PFDF). The current deterministic methods used to handle these problems are based on the concept of continuous variables; therefore, the methods always transform the original model into another programming model (e.g., DC programming, convex programming) and solve them with a commercial solver. As the nature of a discrete variable is quite different from that of a continuous one, developing a novel method to address the above mentioned problems is necessary. This study proposes a concise and efficient method that linearizes PFDF term into a set of linear inequalities directly without redundant transformation. Further, the proposed method only requires the logarithmic numbers of binary variables and constraints. Numerical examples demonstrate that the proposed formulation significantly outperforms current approaches.
机译：在本文中，开发了一种对数方法来解决包含自由符号离散函数（PFDF）乘积的优化问题。当前用于处理这些问题的确定性方法是基于连续变量的概念。因此，这些方法总是将原始模型转换为另一种编程模型（例如DC编程，凸编程），并使用商用求解器进行求解。由于离散变量的性质与连续变量的性质完全不同，因此有必要开发一种新颖的方法来解决上述问题。这项研究提出了一种简洁有效的方法，该方法无需冗余转换即可直接将PFDF项线性化为一组线性不等式。此外，所提出的方法仅需要二进制变量和约束的对数。数值示例表明，所提出的公式明显优于现有方法。

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