Primal-Dual Accelerated Mirror-Descent Method for Constrained Bilinear Saddle-Point Problems

Weijian Li; Xianlin Zeng; Lacra Pavel

doi:10.1109/TAC.2025.3609398

Primal-Dual Accelerated Mirror-Descent Method for Constrained Bilinear Saddle-Point Problems

Weijian Li
, Xianlin Zeng
, Lacra Pavel^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We develop a first-order accelerated algorithm for a class of constrained bilinear saddle-point problems with applications to network systems. The algorithm is a modified time-varying primal-dual version of an accelerated mirror-descent dynamics. It deals with constraints such as simplices and convex set constraints effectively, and converges with a rate of O(1/t²). Furthermore, we employ the acceleration scheme for constrained distributed optimization and bilinear zero-sum games, and obtain two variants of distributed accelerated algorithms.

Original language	English
Pages (from-to)	1373-1380
Number of pages	8
Journal	IEEE Transactions on Automatic Control
Volume	71
Issue number	2
DOIs	https://doi.org/10.1109/TAC.2025.3609398
Publication status	Published - 2026
Externally published	Yes

Keywords

Accelerated mirror-descent dynamics
constrained bilinear saddle-point problem (BSPP)
distributed optimization/game
primal-dual method

Access to Document

10.1109/TAC.2025.3609398

Cite this

@article{1b28e227e77449f48f8599234392109d,

title = "Primal-Dual Accelerated Mirror-Descent Method for Constrained Bilinear Saddle-Point Problems",

abstract = "We develop a first-order accelerated algorithm for a class of constrained bilinear saddle-point problems with applications to network systems. The algorithm is a modified time-varying primal-dual version of an accelerated mirror-descent dynamics. It deals with constraints such as simplices and convex set constraints effectively, and converges with a rate of O(1/t2). Furthermore, we employ the acceleration scheme for constrained distributed optimization and bilinear zero-sum games, and obtain two variants of distributed accelerated algorithms.",

keywords = "Accelerated mirror-descent dynamics, constrained bilinear saddle-point problem (BSPP), distributed optimization/game, primal-dual method",

author = "Weijian Li and Xianlin Zeng and Lacra Pavel",

note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2026",

doi = "10.1109/TAC.2025.3609398",

language = "English",

volume = "71",

pages = "1373--1380",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "2",

}

TY - JOUR

T1 - Primal-Dual Accelerated Mirror-Descent Method for Constrained Bilinear Saddle-Point Problems

AU - Li, Weijian

AU - Zeng, Xianlin

AU - Pavel, Lacra

PY - 2026

Y1 - 2026

N2 - We develop a first-order accelerated algorithm for a class of constrained bilinear saddle-point problems with applications to network systems. The algorithm is a modified time-varying primal-dual version of an accelerated mirror-descent dynamics. It deals with constraints such as simplices and convex set constraints effectively, and converges with a rate of O(1/t2). Furthermore, we employ the acceleration scheme for constrained distributed optimization and bilinear zero-sum games, and obtain two variants of distributed accelerated algorithms.

AB - We develop a first-order accelerated algorithm for a class of constrained bilinear saddle-point problems with applications to network systems. The algorithm is a modified time-varying primal-dual version of an accelerated mirror-descent dynamics. It deals with constraints such as simplices and convex set constraints effectively, and converges with a rate of O(1/t2). Furthermore, we employ the acceleration scheme for constrained distributed optimization and bilinear zero-sum games, and obtain two variants of distributed accelerated algorithms.

KW - Accelerated mirror-descent dynamics

KW - constrained bilinear saddle-point problem (BSPP)

KW - distributed optimization/game

KW - primal-dual method

UR - https://www.scopus.com/pages/publications/105015725425

U2 - 10.1109/TAC.2025.3609398

DO - 10.1109/TAC.2025.3609398

M3 - Article

AN - SCOPUS:105015725425

SN - 0018-9286

VL - 71

SP - 1373

EP - 1380

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 2

ER -

Primal-Dual Accelerated Mirror-Descent Method for Constrained Bilinear Saddle-Point Problems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this