A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces
将一种针对局部Lipschitz连续多目标优化问题的高效方法从有限维推广到一般希尔伯特空间，通过迭代计算Pareto临界点，并证明了收敛性，数值实验展示了在障碍问题多目标最优控制中的效率。
Abstract The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from Gebken and Peitz (J Optim Theory Appl 188:696–723, 2021) 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 Clarke 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.