DualBi：一种用于具有标量复杂约束的非凸问题的对偶二分算法
DualBi: A dual bisection algorithm for non-convex problems with a scalar complicating constraint
AI总结：
本文提出DualBi对偶二分算法，通过迭代更新标量对偶变量求解具有标量复杂约束的非凸优化问题，并应用于多智能体MILPs实现去中心化求解，仿真验证其优于现有对偶方法。
摘要：
本文研究以标量复杂约束为特征的非凸约束优化问题。我们针对对偶问题提出了一种迭代二分方法（DualBi Algorithm），该方法能够恢复可行的原始解，且其性能在迭代过程中逐步提升。将该方法应用于具有标量耦合约束的多智能体问题，可得到一种去中心化求解方案：由中央单元负责更新（标量）对偶变量，而各智能体计算各自的局部原始变量。在多智能体混合整数线性规划（MILPs）情形下，仿真实验展示了所提方法与当前最先进的基于对偶性的方法相比的性能表现。
英文摘要：
This paper addresses non-convex constrained optimization problems that are characterized by a scalar complicating constraint. We propose an iterative bisection method for the dual problem (DualBi Algorithm) that recovers a feasible primal solution, with a performance that is progressively improving throughout iterations. Application to multi-agent problems with a scalar coupling constraint results in a decentralized resolution scheme where a central unit is in charge of the update of the (scalar) dual variable while agents compute their local primal variables. In the case of multi-agent MILPs, simulations showcase the performance of the proposed method compared with state-of-the-art duality-based approaches.
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