ABSTRACT

We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral approximation of the upper image. It is a modification of the primal algorithm presented by Löhne, Rudloff, and Ulus in 2014. There, vertices of an already known outer approximation are successively cutoff to improve the approximation error. We propose a new and efficient selection rule for deciding which vertex to cutoff. Numerical examples are provided which illustrate that this method may solve fewer scalar problems overall and therefore may be faster while achieving the same approximation quality.

摘要

我们提出了一种近似求解有界凸向量优化问题的算法。该算法提供了上部图像的外部和内部多面体近似。它是 Löhne、Rudloff 和 Ulus 在 2014 年提出的原始算法的修改。在那里，已知外部近似的顶点被连续截断以改善近似误差。我们提出了一种新的有效选择规则来决定要切断哪个顶点。提供了数值示例，说明该方法总体上可以解决较少的标量问题，因此在实现相同近似质量的同时可能更快。