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arXiv · 2103.12937

Inertial primal-dual methods for linear equality constrained convex optimization problems

Xin He·Rong Hu·Ya-Ping Fang
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Abstract

In this paper, we propose an inertial accelerated primal-dual method for the linear equality constrained convex optimization problem. When the objective function has a ``nonsmooth + smooth'' composite structure, we further propose an inexact inertial primal-dual method by linearizing the smooth individual function and solving the subproblem inexactly. Assuming merely convexity, we prove that the proposed methods enjoy $\mathcal{O}(1/k^2)$ convergence rate on the objective residual and the feasibility violation in the primal model. Numerical results are reported to demonstrate the validity of the proposed methods.

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Xin He, Rong Hu, Ya-Ping Fang. 2021-03-24. Inertial primal-dual methods for linear equality constrained convex optimization problems. https://arxiv.org/abs/2103.12937

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