A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces
arxiv(2024)
摘要
The efficient optimization method for locally Lipschitz continuous
multiobjective optimization problems from [1] is extended from
finite-dimensional problems to general Hilbert spaces. The method iteratively
computes Pareto critical points, where in each iteration, an approximation of
the subdifferential is computed in an efficient manner and then used to compute
a common descent direction for all objective functions. To prove convergence,
we present some new optimality results for nonsmooth multiobjective
optimization problems in Hilbert spaces. Using these, we can show that every
accumulation point of the sequence generated by our algorithm is Pareto
critical under common assumptions. Computational efficiency for finding Pareto
critical points is numerically demonstrated for multiobjective optimal control
of an obstacle problem.
更多查看译文
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要