One of the commonly used techniques for tackling the nonconvex optimization problems in which all the nonlinear terms are univariate is the piecewise linear approximation by which the nonlinear terms are reformulated. The performance of the linearization technique primarily depends on the quantities of variables and constraints required in the formulation of a piecewise linear function. The state-of-the-art linearization method introduces \(2\lceil \log _2 m\rceil\) inequality constraints, where m is the number of line segments in the constructed piecewise linear function. This study proposes an effective alternative logarithmic scheme by which no inequality constraint is incurred. The price that more continuous variables are needed in the proposed scheme than in the state-of-the-art method is less than offset by the simultaneous inclusion of a system of equality constraints satisfying the canonical form and the absence of any inequality constraint. Our numerical experiments demonstrate that the developed scheme has the computational superiority, the degree of which increases with m.

用于解决所有非线性项都是单变量的非凸优化问题的常用技术之一是分段线性近似，通过它重新表述非线性项。线性化技术的性能主要取决于制定分段线性函数所需的变量和约束的数量。最先进的线性化方法引入了\(2\lceil \log _2 m\rceil\)不等式约束，其中m是构建的分段线性函数中的线段数。本研究提出了一种有效的替代对数方案，由此不会产生不等式约束。与最先进的方法相比，所提出的方案中需要更多连续变量的代价不会被同时包含满足规范形式的等式约束系统和不存在任何不等式约束所抵消。我们的数值实验表明，所开发的方案具有计算优势，其程度随m增加。