bzhangcw / abip-lp

Admm-based Interior Point Method for Linear Programming

ABIP

ADMM-based Interior Point Method for Linear and Conic Programming

ABIP is a new framework that applies alternating direction method of multipliers (ADMM) to implement interior point method (IPM) for solving large-scale linear programs (LP) and conic programs (QCP).

ABIP(LP) was initially developed by Tianyi Lin (https://github.com/tyDLin) and is currently maintained by LEAVES optimization software platform.

Version

Current version of ABIP is 2.0

v2.0 (ABIP+)

1. Added support for QCP
2. Improved LP solver

v1.0

1. ABIP for large scale linear programming problems

Reference

• Lin, Tianyi, et al. "An ADMM-based interior-point method for large-scale linear programming." Optimization Methods and Software (2020): 1-36.
• Deng, Qi, et al. "New Developments of ADMM-based Interior Point Methods for Linear Programming and Conic Programming." arXiv preprint arXiv:2209.01793 (2022).

Installation

To install ABIP, use install.m script in the main direction.

For QCP solver, user needs to specify MKL path in

mkl_path = ''; % '/opt/intel/oneapi/mkl'

How to call ABIP

ABIP accepts standard sedumi format defined using $A, b, c, K$.

To call it, use

[x, y, s, info] = abip(data, K, params)

Parameter	Explanation
verbose	If log is turned on
normalize	Whether to perform data scaling before the solve
pcg	Whether to use iterative solver for linear systems
max_admm_iter	Maximum ADMM iteration
max_ipm_iter	Maximum IPM iteration
timelimit	Time limit
tol	Relative tolerance of convergence
solver	Choose which solver to use, -1: automatic 1: force QCP

Current developers

ABIP-LP

Chenyu Xue (Phd. student at RIIS, Shanghai University of Finance and Economics. Email: [e-mail])

ABIP-QCP

Jinsong Liu (Phd. student at RIIS, Shanghai University of Finance and Economics. Email: [e-mail])

Tianhao Liu (Phd. student at RIIS, Shanghai University of Finance and Economics. Email: [e-mail])

Testing

Chuwen Zhang (Phd. student at RIIS, Shanghai University of Finance and Economics. Email: [e-mail])

Interface

Wenzhi Gao (Master student at SIME, Shanghai University of Finance and Economics. Email: [e-mail])