The problem of minimizing the difference of two convex functions is called polyhedral d.c. optimization problem if at least one of the two component functions is polyhedral. We characterize the existence of global optimal solutions of polyhedral d.c. optimization problems. This result is used to show that, whenever the existence of an optimal solution can be certified, polyhedral d.c. optimization problems can be solved by certain concave minimization algorithms. No further assumptions are necessary in case of the first component being polyhedral and just some mild assumptions to the first component are required for the case where the second component is polyhedral. In case of both component functions being polyhedral, we obtain a primal and dual existence test and a primal and dual solution procedure. Numerical examples are discussed.

如果两个分量函数中的至少一个是多面体的，则使两个凸函数之间的差最小化的问题称为多面体dc优化问题。我们刻画了多面体直流优化问题的全局最优解的存在。该结果用于表明，只要可以证明存在最优解，就可以通过某些凹面最小化算法来解决多面体直流优化问题。如果第一组分是多面体的，则不需要进一步的假设，而对于第二组分是多面体的情况，仅需要对第一组分进行一些温和的假定即可。在两个分量函数都是多面体的情况下，我们获得了原始和对偶存在性检验以及原始和对偶求解过程。讨论了数值示例。