Convex optimization with equality and inequality constraints is a ubiquitous problem in several optimization and control problems in large-scale systems. Recently there has been a lot of interest in establishing accelerated convergence of the loss function. A class of high-order tuners was recently proposed in an effort to lead to accelerated convergence for the case when no constraints are present. In this paper, we propose a new high-order tuner that can accommodate the presence of equality constraints. In order to accommodate the underlying box constraints, time-varying gains are introduced in the high-order tuner which leverage convexity and ensure anytime feasibility of the constraints. Numerical examples are provided to support the theoretical derivations.

翻译：等式约束与不等式约束的凸优化是大规模系统中多个优化与控制问题中的常见问题。近年来，损失函数加速收敛的建立引起了广泛关注。为应对无约束情况下的加速收敛问题，近期提出了一类高阶调节器。本文提出了一种能够处理等式约束的新型高阶调节器。为适应潜在的盒约束，在高阶调节器中引入了时变增益，利用凸性确保约束的随时可行性。数值算例支持了理论推导结果。