具有不等式约束的优化问题的微分方程方法
The Differential Equation Method for Solving the Optimization with the Inequality Constraints
DOI: 10.12677/PM.2020.109103, PDF,    国家自然科学基金支持
作者: 王 程, 胡议欣, 赵元皓, 韩 笑, 王 莉：沈阳航空航天大学理学院，辽宁 沈阳
关键词: 优化问题；拉格朗日函数；投影算子；微分方程方法；Optimization Problem； Lagrange Function； Projection Operator； Differential Equation Method
摘要: 本文研究了具有不等式约束的优化问题的微分方程方法。首先建立优化问题的拉格朗日函数，运用鞍点的性质和投影算子，将原始的优化问题转化为等式方程。再利用等式方程建立微分方程系统，并证明了该微分方程系统的轨迹的聚点是原始的优化问题的解。
Abstract: This paper presents a class of differential equation method for solving the optimization with the inequality constraints. Firstly, the Lagrange function for the optimization is established, then the original convex optimization can be transformed to be the equations based on the nature of saddle point and the projection operator. The differential equation systems are obtained by applying the equations, and the convergence of the trajectories of these differential equation systems are proved.
文章引用：王程, 胡议欣, 赵元皓, 韩笑, 王莉. 具有不等式约束的优化问题的微分方程方法[J]. 理论数学, 2020, 10(9): 889-896. https://doi.org/10.12677/PM.2020.109103

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