OSQP: An operator splitting solver for quadratic programs

B Stellato, G Banjac, P Goulart, A Bemporad… - Mathematical …, 2020 - Springer
We present a general-purpose solver for convex quadratic programs based on the
alternating direction method of multipliers, employing a novel operator splitting technique …

Infeasibility detection in the alternating direction method of multipliers for convex optimization

G Banjac, P Goulart, B Stellato, S Boyd - Journal of Optimization Theory …, 2019 - Springer
The alternating direction method of multipliers is a powerful operator splitting technique for
solving structured optimization problems. For convex optimization problems, it is well known …

End-to-end learning to warm-start for real-time quadratic optimization

R Sambharya, G Hall, B Amos… - Learning for Dynamics …, 2023 - proceedings.mlr.press
First-order methods are widely used to solve convex quadratic programs (QPs) in real-time
appli-cations because of their low per-iteration cost. However, they can suffer from slow …

Time-varying convex optimization via time-varying averaged operators

A Simonetto - arXiv preprint arXiv:1704.07338, 2017 - arxiv.org
Devising efficient algorithms that track the optimizers of continuously varying convex
optimization problems is key in many applications. A possible strategy is to sample the time …

Scaled relative graphs: Nonexpansive operators via 2D Euclidean geometry

EK Ryu, R Hannah, W Yin - Mathematical Programming, 2022 - Springer
Many iterative methods in applied mathematics can be thought of as fixed-point iterations,
and such algorithms are usually analyzed analytically, with inequalities. In this paper, we …

Restart FISTA with global linear convergence

T Alamo, D Limon, P Krupa - 2019 18th European Control …, 2019 - ieeexplore.ieee.org
Fast Iterative Shrinking-Threshold Algorithm (FISTA) is a popular fast gradient descent
method (FGM) in the field of large scale convex optimization problems. However, it can …

Tight coefficients of averaged operators via scaled relative graph

X Huang, EK Ryu, W Yin - Journal of Mathematical Analysis and …, 2020 - Elsevier
Many iterative methods in optimization are fixed-point iterations with averaged operators. As
such methods converge at an O (1/k) rate with the constant determined by the averagedness …

Gradient based restart FISTA

T Alamo, P Krupa, D Limon - 2019 IEEE 58th Conference on …, 2019 - ieeexplore.ieee.org
Fast gradient methods (FGM) are very popular in the field of large scale convex optimization
problems. Recently, it has been shown that restart strategies can guarantee global linear …

A first-order numerical algorithm without matrix operations

M Adil, R Madani, S Tavakkol, A Davoudi - arXiv preprint arXiv …, 2022 - arxiv.org
This paper offers a matrix-free first-order numerical method to solve large-scale conic
optimization problems. Solving systems of linear equations pose the most computationally …

General optimal step-size and initializations for admm: A proximal operator view

Y Ran - arXiv preprint arXiv:2309.10124, 2023 - arxiv.org
In this work, we solve a 48-year open problem by presenting the first general optimal step-
size choice for Alternating Direction Method of Multipliers (ADMM). For a convex problem …