Alternating Direction Method with Increasing Penalty for Clustering (ADMIPC)

ADMIPC is an ADMM algorithm with increasing penalty for detecting non-overlapping communities in a partially observed undirected graphs. For details of the ADMIPC, refer to the paper. Download ADMIPC v1

First-order Augmented Lagrangian (FAL) Algorithm

FAL is a first-order algorithm to solve Basis Pursuit (BP) problem:

\[\large \min_{x\in\mathbb{R}^n}\{\|x\|_1:\ \|Ax-b\|_2\leq\delta\}. \]

Download FAL v1 The README file describes the setup and the details of the code. For more details, refer to the paper.

Partially Smooth Proximal Gradient (PSPG) Algorithm

PSPG is a first-order algorithm to solve Stable Principal Component Pursuit (SPCP) problem:

\[\large \min_{X,S\in\mathbb{R}^{m\times n}}\{\|X\|_*+\xi\|S\|_1:\ \|X+S-D\|_F\leq\delta\}. \]

The first term in the objective function is equal to the sum of singular values of \(X\) and the second term is equal to sum of absolute values of all the components of \(S\). Smooting one of the terms in the objective function, it achieves \(\mathcal{O}(1/\epsilon)\) iteration complexity. Download PSPG v1 The README file describes the setup and the details of the code. For details of the PSPG, refer to the paper.

Alternating Direction Method with Increasing Penalty (ADMIP)

ADMIP is an ADMM algorithm with increasing penalty to solve Stable Principal Component Pursuit (SPCP) problem. For details of the ADMIP, refer to the paper. Note: In an earlier preprint, we named it as Non-Smooth Augmented (NSA) algorithm. Download NSA v1 The README file describes the setup and the details of the code.