A class of non-convex optimization problems with DC objective function isstudied, where DC stands for being representable as the difference $f=g-h$ oftwo convex functions $g$ and $h$. In particular, we deal with the special casewhere one of the two convex functions $g$ or $h$ is polyhedral. In case $g$ ispolyhedral, we show that a solution of the DC program can be obtained from asolution of an associated polyhedral projection problem. In case $h$ ispolyhedral, we prove that a solution of the DC program can be obtained bysolving a polyhedral projection problem and finitely many convex programs.Since polyhedral projection is equivalent to multiple objective linearprogramming (MOLP), a MOLP solver (in the second case together with a convexprogramming solver) can be used to solve instances of DC programs withpolyhedral component. Numerical examples are provided, among them anapplication to locational analysis.
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机译：研究了一类具有DC目标函数的非凸优化问题，其中DC代表可表示为两个凸函数$ g $和$ h $的差$ f = g-h $。特别是，我们处理两个凸函数$ g $或$ h $之一是多面体的特殊情况。在$ g $是多面体的情况下，我们表明可以从一个相关的多面体投影问题的解决方案中获得DC程序的一个解决方案。在$ h $是多面体的情况下，我们证明可以通过求解多面体投影问题和有限的多个凸规划来获得DC程序的解。由于多面体投影等效于多目标线性规划（MOLP），因此MOLP求解器（第二案例与凸编程求解器一起使用）可用于求解具有多面体成分的DC程序实例。提供了数值示例，其中包括位置分析的应用。
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