Decision Space Decomposition for Multiobjective Optimization
受参数化分解定理和块坐标下降法启发，提出一种将偏序集最小元集合分解为子集的方法，并应用于凸多目标优化问题，证明其在Painlevé-Kuratowski意义下的集合收敛，包含双目标二次优化的特例。
Abstract Being inspired by the parametric decomposition theorem for multiobjective optimization problems (MOPs) of Cuenca Mira and Miguel García (2017), and by the block-coordinate descent method for single objective optimization problems, we present a decomposition theorem for computing the set of minimal elements of a partially ordered set. This set is decomposed into subsets whose minimal elements are used to retrieve the overall minimal elements. We apply this approach to convex MOPs decomposing their decision space into lines and prove the set convergence of this method in the Painlevé-Kuratowski sense. A special case for biobjective quadratic optimization problems is included.