| 引用本文: | 孟敏,李修贤.Aug-PDG: 带不等式约束凸优化算法的线性收敛性 （英文）[J].控制理论与应用,2022,39(10):1969~1977.[点击复制] |
| MENG Min,LI Xiu-xian.Aug-PDG: Linear Convergence of Convex Optimization with Inequality Constraints[J].Control Theory and Technology,2022,39(10):1969~1977.[点击复制] |
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| Aug-PDG: 带不等式约束凸优化算法的线性收敛性 （英文） |
| Aug-PDG: Linear Convergence of Convex Optimization with Inequality Constraints |
| 摘要点击 1648 全文点击 386 投稿时间：2021-07-02 修订日期：2022-10-11 |
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| DOI编号 10.7641/CTA.2021.10583 |
| 2022,39(10):1969-1977 |
| 中文关键词 凸优化 非线性约束 线性收敛 增广原始-对偶梯度算法 |
| 英文关键词 Convex optimization, nonlinear inequality constraints, linear convergence, augmented primal-dual gradient algorithm |
| 基金项目 上海市浦江计划（21PJ1413100）、国家自然科学基金（62003243，62103305）、上海市 上海市科委科技重大专项（2021SHZDZX0100） 1132101）、中国科协青年精英科学家资助计划（YESS20200136）和中央高校基本科研业务费基金（22120210096） |
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| 中文摘要 |
| 原始-对偶梯度算法广泛应用于求解带约束的凸优化问题, 大部分文献仅证明了该算法的收敛性, 而没有分析其收敛速度. 因此, 本文研究了求解带有不等式约束凸优化的一类离散算法, 即增广原始-对偶梯度算法 (Aug-PDG), 证明了Aug-PDG 算法在一些较弱的假设条件下可以半全局线性收敛到最优解, 并明确给出了算法中步长的上界. 最后, 数值算例证实了所得理论结果的有效性. |
| 英文摘要 |
| The primal-dual gradient algorithm has been widely employed for solving constrained optimization problems. While the convergence of this algorithm was proved in most references, it is less investigated whether it is globally linearly convergent. Therefore, this paper studies convergence rate of its variant, i.e., the augmented primal-dual gradient algorithm (Aug-PDG), for handling the convex optimization problem with general convex inequality constraints. Specifically, it is shown that Aug-PDG can converge semi-globally to the optimizer at a linear rate under some mild assumptions and an explicit bound is provided for the stepsize in this algorithm. Finally, a numerical example is presented to illustrate the efficacy of the theoretical finding. |
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