No abstract

No abstract

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.

This paper presents a framework to solve constrained optimization problems in an accelerated manner based on High-Order Tuners (HT). Our approach is based on reformulating the original constrained problem as the unconstrained optimization of a loss function. We start with convex optimization problems and identify the conditions under which the loss function is convex. Building on the insight that the loss function could be convex even if the original optimization problem is not, we extend our approach to a class of nonconvex optimization problems. The use of a HT together with this approach enables us to achieve a convergence rate better than state-of-the-art gradient-based methods. Moreover, for equality-constrained optimization problems, the proposed method ensures that the state remains feasible throughout the evolution, regardless of the convexity of the original problem.