论文标题
混合整数凸优化的精确增强拉格朗日二元性
Exact augmented Lagrangian duality for mixed integer convex optimization
论文作者
论文摘要
增强拉格朗日二重奏增强了经典的拉格朗日二重奏，其非负性非线性惩罚函数违反了放松/双重的约束，以减少双重性差距。我们调查了混合整数凸优化问题具有使用尖锐的增强功能（规范作为增强惩罚函数）具有确切的惩罚表示的案例。我们提出了一种可推广的建设性证明技术，用于证明使用关联的值函数在特定条件下为混合整数凸面程序证明存在精确的罚款。这概括了MILP（Feizollahi，Ahmed和Sun，2017年）和MIQP（GU，Ahmed和Dey 2020）的最新结果，同时还为这些情况下提供了上述额外罚款参数的替代证明。
Augmented Lagrangian dual augments the classical Lagrangian dual with a non-negative non-linear penalty function of the violation of the relaxed/dualized constraints in order to reduce the duality gap. We investigate the cases in which mixed integer convex optimization problems have an exact penalty representation using sharp augmenting functions (norms as augmenting penalty functions). We present a generalizable constructive proof technique for proving existence of exact penalty representations for mixed integer convex programs under specific conditions using the associated value functions. This generalizes the recent results for MILP (Feizollahi, Ahmed and Sun, 2017) and MIQP (Gu, Ahmed and Dey 2020) whilst also providing an alternative proof for the aforementioned along with quantification of the finite penalty parameter in these cases.
