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Complexity iteration analysis for strongly convex multi-objective optimization using a Newton path-following procedure
Optimization Letters ( IF 1.6 ) Pub Date : 2020-07-23 , DOI: 10.1007/s11590-020-01623-x El-Houcine Bergou , Youssef Diouane , Vyacheslav Kungurtsev
中文翻译:
牛顿路径跟随过程的强凸多目标优化复杂度迭代分析
更新日期:2020-07-24
Optimization Letters ( IF 1.6 ) Pub Date : 2020-07-23 , DOI: 10.1007/s11590-020-01623-x El-Houcine Bergou , Youssef Diouane , Vyacheslav Kungurtsev
In this note, we consider the iteration complexity of solving strongly convex multi-objective optimization problems. We discuss the precise meaning of this problem, noting that its definition is ambiguous, and focus on the most natural notion of finding a set of Pareto optimal points across a grid of scalarized problems. We prove that, in most cases, performing sensitivity based path-following after obtaining one solution is the optimal strategy for this task in terms of iteration complexity.
中文翻译:
牛顿路径跟随过程的强凸多目标优化复杂度迭代分析
在本文中,我们考虑了解决强凸多目标优化问题的迭代复杂性。我们讨论了该问题的确切含义,并指出其定义是模棱两可的,并着眼于最自然的概念,即在一个标量问题网格上找到一组帕累托最优点。我们证明,在大多数情况下,就迭代复杂度而言,获得一种解决方案后执行基于敏感性的路径跟随是此任务的最佳策略。