An improved proximal primal–dual ALM-based algorithm with convex combination proximal centers for equality-constrained convex programming in basis pursuit practical problems

Abstract

In this paper, we propose a novel proximal point Lagrangian-based method for solving convex programming problems with linear equality constraints, where the proximal centers are constructed using convex combinations of the iterates. The new method preserves all the favorable characteristics of customized proximal point algorithm, including convergence of both the primal and dual iterates, as well as the ability to derive closed-form solutions for subproblems under certain conditions. Furthermore, we prove the global convergence and establish an $O(1/K)$ ergodic sublinear convergence rate of our algorithm under mild assumptions. Finally, numerical experiments conducted on basis pursuit and equality-constrained quadratic programming problems demonstrate the superior performance of our proposed algorithm.