论文标题
针对受限的单调包含物的原始偶对局部逆向分裂：随机编程和平均现场游戏的应用
A Primal-Dual Partial Inverse Splitting for Constrained Monotone Inclusions: Applications to stochastic Programming and Mean Field Games
论文作者
论文摘要
在这项工作中，我们研究了涉及正常锥到封闭的矢量子空间的受约束单调包容性以及有关原始溶液的先验信息。我们通过强加解决方案属于平均非专用映射的固定点集建模。我们使用涉及部分逆操作员的辅助包含来表征解决方案。然后，我们提出了原始的偶有部分反向分裂，并证明了其弱收敛到包含的解决方案，从而在文献中推广了几种方法。在两个非平滑凸优化问题中说明了所提出的方法的效率，其约束具有向量子空间结构。最后，采用所提出的算法来找到转运网络中随机弧容量扩展问题的解决方案。
In this work we study a constrained monotone inclusion involving the normal cone to a closed vector subspace and a priori information on primal solutions. We model this information by imposing that solutions belongs to the fixed point set of an averaged nonexpansive mapping. We characterize the solutions using an auxiliary inclusion that involves the partial inverse operator. Then, we propose the primal-dual partial inverse splitting and we prove its weak convergence to a solution of the inclusion, generalizing several methods in the literature. The efficiency of the proposed method is illustrated in two non-smooth convex optimization problems whose constraints have vector subspace structure. Finally, the proposed algorithm is applied to find a solution to a stochastic arc capacity expansion problem in transport networks.
