A Warped Resolvent Algorithm to Construct Nash Equilibria

Warped Proximal Iterations for Monotone Inclusions

Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion, called warped resolvent, which is constructed with the help of an auxiliary operator. The properties of warped resolvents are investigated and connections are made with existing notions. Abstract weak and strong convergence principles based on warped resolvents are proposed and shown to not only provide a synthetic view of splitting algorithms but to also co…

非精确扭曲预解迭代

Inexact Warped Resolvent iterations

提出基于相对误差准则的非精确扭曲预解迭代算法，统一多种经典分裂方法，证明弱收敛、强收敛和线性收敛，并在鞍点与凸优化问题中验证计算优势。

利用算子对的单调性求解非单调包含问题

Solving Non-Monotone Inclusions Using Monotonicity of Pairs of Operators

本文利用算子对单调性，提出广义近端点算法求解非单调包含问题，并证明其在温和条件下的弱、强及线性收敛性。

带动量校正的非线性前向-后向分裂方法

Nonlinear Forward-Backward Splitting with Momentum Correction

针对非线性预解式算法的收敛问题，本文以非线性动量项替代校正投影步骤，降低迭代成本，并统一推导、扩展多种前向-后向及原始-对偶方法。

利用对单调性求解两个非单调算子之和问题的分裂算法

Splitting Algorithms Using Pairs Monotonicity to Solve the Sum of Two Non-monotone Operators Problem

本文针对实希尔伯特空间中两个非单调算子之和的零点问题，基于对单调性提出广义前向-后向和Tseng分裂算法，证明其弱、强及线性收敛，并通过数值实验验证有效性。