LADEL
swMATH ID:  43730 
Software Authors:  Hermans, Ben; Themelis, Andreas; Patrinos, Panagiotis 
Description:  QPALM: a proximal augmented Lagrangian method for nonconvex quadratic programs. We propose QPALM, a nonconvex quadratic programming (QP) solver based on the proximal augmented Lagrangian method. This method solves a sequence of inner subproblems which can be enforced to be strongly convex and which therefore admit a unique solution. The resulting steps are shown to be equivalent to inexact proximal point iterations on the extendedrealvalued cost function, which allows for a fairly simple analysis where convergence to a stationary point at an Rlinear rate is shown. The QPALM algorithm solves the subproblems iteratively using semismooth Newton directions and an exact linesearch. The former can be computed efficiently in most iterations by making use of suitable factorization update routines, while the latter requires the zero of a monotone, onedimensional, piecewise affine function. QPALM is implemented in opensource C code, with tailored linear algebra routines for the factorization in a selfwritten package LADEL. The resulting implementation is shown to be extremely robust in numerical simulations, solving all of the MarosMeszaros problems and finding a stationary point for most of the nonconvex QPs in the Cutest test set. Furthermore, it is shown to be competitive against stateoftheart convex QP solvers in typical QPs arising from application domains such as portfolio optimization and model predictive control. As such, QPALM strikes a unique balance between solving both easy and hard problems efficiently. 
Homepage:  https://arxiv.org/abs/2010.02653 
Source Code:  https://github.com/Benny44/LADEL 
Keywords:  nonconvex QPs; proximal augmented Lagrangian; semismooth Newton method; exact linesearch; factorization updates 
Related Software:  Matlab; NCOPT; OOQP; BPMPD; OSQP; QuadProgBB; GALAHAD; LDL; CSparse; NETLIB LP Test Set; lobpcg.m; ALGENCAN; NewtonKKTqp; Ipopt; QPALM; HPIPM; CUTEst; qpOASES; Mosek; CHOLMOD 
Cited in:  1 Document 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

QPALM: a proximal augmented Lagrangian method for nonconvex quadratic programs. Zbl 1496.90032 Hermans, Ben; Themelis, Andreas; Patrinos, Panagiotis 
2022

Cited by 3 Authors
1  Hermans, Ben 
1  Patrinos, Panagiotis 
1  Themelis, Andreas 
Cited in 1 Serial
1  Mathematical Programming Computation 
Cited in 2 Fields
1  Calculus of variations and optimal control; optimization (49XX) 
1  Operations research, mathematical programming (90XX) 