发表机构
The University of Arizona（亚利桑那大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对均衡条件作用于变换状态的问题，提出基于投影残差重构的残差反馈方法，无需求逆状态映射，实现一步法与预测-校正法的最优迭代残差率及线性收敛，并扩展至广义拟变分不等式。
AI 中文摘要
受网络系统中均衡条件作用于受调节状态而非直接作用于决策变量的启发，我们研究了变换状态的一般变分不等式。利用投影残差重构，我们开发了在决策空间中运行且无需对状态映射 $H$ 求逆的残差反馈方法。对于一步方法，我们在解受限余强制条件下建立了 $\u039f(T^{-1/2})$ 的最优迭代残差率，并在解受限强单调性和残差 Lipschitz 连续性条件下建立了线性收敛。我们还针对在单调性和 Lipschitz 连续性条件下应用于诱导 GVI 残差的预测-校正方法，获得了 $\u039f(T^{-1/2})$ 的最优迭代残差率。这些假设直接施加于可计算的残差，并通过仿射网络和秩亏示例加以说明。最后，我们将残差框架扩展到具有决策依赖可行集的一般化拟变分不等式。
英文摘要
Motivated by networked systems in which equilibrium conditions apply to a regulated state rather than directly to the decision variable, we study transformed-state general variational inequalities. Using a projection-residual reformulation, we develop residual feedback methods that operate in the decision space without inverting the state mapping $H$. For a one-step method, we establish an $\mathcal{O}(T^{-1/2})$ best-iterate residual rate under solution-restricted cocoercivity and linear convergence under solution-restricted strong monotonicity and residual Lipschitz continuity. We also obtain an $\mathcal{O}(T^{-1/2})$ best-iterate residual rate for a predictor-corrector method applied to the induced GVI residual under monotonicity and Lipschitz continuity. The assumptions are imposed directly on the computable residual and are illustrated by affine network and rank-deficient examples. Finally, we extend the residual framework to generalized quasi-variational inequalities with decision-dependent feasible sets.
