论文标题
AUG-PDG：凸优化的线性收敛与不等式约束
Aug-PDG: Linear Convergence of Convex Optimization with Inequality Constraints
论文作者
论文摘要
本文研究了凸的优化问题，其中一般凸不平等约束。为了解决这个问题，研究和分析了一种离散的时间算法，称为增强原始偶梯度算法（AUG-PDG）。结果表明，在某些温和的假设下，Aug-PDG可以以线性速率将半全球收敛到优化器，例如目标函数的二次梯度生长条件，这严格比强凸高。据我们所知，本文是第一个在离散时间设置中为所研究问题建立线性收敛的，在该设置中为STEPISE提供了明确的界限。最后，提出了一个数值示例，以说明理论发现的功效。
This paper investigates the convex optimization problem with general convex inequality constraints. To cope with this problem, a discrete-time algorithm, called augmented primal-dual gradient algorithm (Aug-PDG), is studied and analyzed. It is shown that Aug-PDG can converge semi-globally to the optimizer at a linear rate under some mild assumptions, such as the quadratic gradient growth condition for the objective function, which is strictly weaker than strong convexity. To our best knowledge, this paper is the first to establish a linear convergence for the studied problem in the discrete-time setting, where an explicit bound is provided for the stepsize. Finally, a numerical example is presented to illustrate the efficacy of the theoretical finding.
