论文标题
深入学习凸向量优化问题的有效边界
Deep Learning the Efficient Frontier of Convex Vector Optimization Problems
论文作者
论文摘要
在本文中，我们设计了一个神经网络体系结构，以近似满足Slater状况的凸矢量优化问题（CVOP）的弱有效边界。提出的机器学习方法提供了弱有效边界的内部和外部近似，以及每个近似有效点处的误差的上限。在数值案例研究中，我们证明了所提出的算法有效地近似于CVOP的真正弱有效的边界。即使对于大问题（即许多目标，变量和约束），这仍然是正确的，从而克服了维度的诅咒。
In this paper, we design a neural network architecture to approximate the weakly efficient frontier of convex vector optimization problems (CVOP) satisfying Slater's condition. The proposed machine learning methodology provides both an inner and outer approximation of the weakly efficient frontier, as well as an upper bound to the error at each approximated efficient point. In numerical case studies we demonstrate that the proposed algorithm is effectively able to approximate the true weakly efficient frontier of CVOPs. This remains true even for large problems (i.e., many objectives, variables, and constraints) and thus overcoming the curse of dimensionality.
