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Nonconvex, lower semicontinuous piecewise linear optimization

机译：非凸，下半连续分段线性优化

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摘要

A branch-and-cut algorithm for solving linear problems with continuous separable piecewise linear cost functions was developed in 2005 by Keha et a]. This algorithm is based on valid inequalities for an SOS2 based formulation of the problem. In this paper we study the extension of the algorithm to the case where the cost function is only lower semicontinuous. We extend the SOS2 based formulation to the lower semicontinuous case and show how the inequalities introduced by Keha et al. can also be used for this new formulation. We also introduce a simple generalization of one of the inequalities introduced by Keha et al. Furthermore, we study the discontinuities caused by fixed charge jumps and introduce two new valid inequalities by extending classical results for fixed charge linear problems. Finally, we report computational results showing how the addition of the developed inequalities can significantly improve the performance of CPLEX when solving these kinds of problems.
机译：Keha等人在2005年开发了一种求解具有连续可分割分段线性成本函数的线性问题的分支切算法。此算法基于问题的基于SOS2的有效不等式。在本文中，我们研究了将算法扩展到成本函数仅为较低半连续性的情况。我们将基于SOS2的公式扩展到较低的半连续情况，并显示Keha等人引入的不等式。也可以用于这种新配方。我们还简单介绍了Keha等人介绍的不等式之一。此外，我们研究了由固定电荷跳跃引起的不连续性，并通过扩展固定电荷线性问题的经典结果引入了两个新的有效不等式。最后，我们报告了计算结果，显示了解决这些问题时如何将已发展的不等式相加可以显着改善CPLEX的性能。

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