Software

Our GitHub page is available at: https://github.com/unc-optimization

Sieve-SDP is a MATAB code to preprocess SDPs based on a simple algorithm developed in “Y. Zhu, G. Pataki, and Q. Tran-Dinh: Sieve-SDP: a simple facial reduction algorithm to preprocess semidefinite programs, https://arxiv.org/abs/1710.08954“.
Sieve-SDP can be downloaded from https://github.com/unc-optimization/SieveSDP.

PAPA-v1.0 is a MATLAB software package for solving constrained convex optimization problems of the form:
where $g$ and $h$ are two convex functions, $\mathbf{B}\in\mathbb{R}^{n\times p}$ , $\mathcal{K}$ is a simple, nonempty, closed, and convex set in $\mathbb{R}^n$ .
Here, we assume that $g$ and $h$ are proximally tractable, i.e., the proximal operators $\mathrm{prox}_{g}$ and $\mathrm{prox}_h$ are efficient to compute (see below).

PAPA aims at solving constrained convex optimization problem for any convex functions $g$ and $h$ , where their proximal operator is provided.
PAPA is developed by Quoc Tran-Dinh at the Department of Statistics and Operations Research, University of North Carolina at Chapel Hill (UNC), North Carolina.
Download: PAPA-v1.0 can be downloaded HERE.
References: The theory and algorithms implemented in PAPA can be found in:
1. Q. Tran Dinh: Proximal Alternating Penalty Algorithms for Nonsmooth Constrained Convex Optimization, Manuscript, STOR-UNC, Nov., 2017. (preprint: https://arxiv.org/pdf/1711.01367.pdf).

LMAOPT-v1.0 is a MATLAB code collection for solving three special cases of the following low-rank matrix optimization problem:
where $\phi$ is a proper, closed and convex function from $\mathbb{R}^l\to\mathbb{R}\cup\{+\infty\}$ , $\mathcal{A}$ is a linear operator from $\mathbb{R}^{m\times n}$ to $\mathbb{R}^l$ , and $B\in\mathbb{R}^l$ is a given observed vector. Here, we are more interested in the case $r \ll \min\{m, n\}$ . Currently, we provide the code to solve three special cases of the above problem:
1. Quadratic loss: $\phi(\cdot) = \frac{1}{2}\Vert\cdot\Vert_2^2$ ;
2. Quadratic loss and symmetric case: $\phi(\cdot) = \frac{1}{2}\Vert\cdot\Vert_2^2$ and $U = V$ ; and
3. Nonsmooth objective loss with tractably proximal operators: For instance, $\phi(\cdot) = \Vert\cdot\Vert_1$ .
LMAOPT is implemented by Quoc Tran-Dinh at the Department of Statistics and Operations Research (STAT&OR), The University of North Carolina at Chapel Hill (UNC). This is a joint work with Zheqi Zhang at STAT & OR, UNC.
Download: LMAOPT-v1.0 can be downloaded HERE.
For further information, please read Readme3.txt.
References: The theory and algorithms implemented in LMAOPT can be found in the following manuscript: Q. Tran-Dinh, and Z. Zhang: Extended Gauss-Newton and Gauss-Newton ADMM algorithms for low-rank matrix optimization. STAT&OR Tech. Report UNC-REPORT-2016.a, (2016). Preprint: http://arxiv.org/abs/1606.03358

These opensource and academic free-of-charge software tools are very useful for research in optimization:

ACADOToolkit – A Toolkit for Automatic Control and Dynamic Optimization (open-source), Boris Houska and Hans Joachim Ferreau (for C++ and Matlab).
IPOPT – Sparse Nonlinear Optimization (open-source).
CasADi – A minimalistic computer algebra system with automatic differentiation (open-source), Joel Andersson (for C++ and Python).
qpOASES – Parametric Quadratic Programming for MPC (open-source), Hans Joachim Ferreau.
TFOCS – Templates for first-order conic solvers, Stephen Becker.
CVX – Disciplined Convex Programming, Michael Grant.
Some of many other software tools that I have been using: SDPT3, SDPNAL+, SeDuMi, SDPA, Mosek, CPLEX, etc.