POGS

Blazing fast convex optimization for machine learning

POGS is 4-14x faster than general-purpose solvers on ML problems like Lasso, Ridge, Logistic Regression, and SVM.

• 4-14x Faster

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  Optimized for ML problems with closed-form proximal operators

• One Line Install

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  pip install pogs — works on macOS, Linux, and Windows

• Pure Python API

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  NumPy arrays in, solution out. No configuration needed.

• CVXPY Integration

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  Auto-detects supported patterns in CVXPY problems

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Performance

Problem	POGS	OSQP	SCS	Clarabel
Lasso (500×300)	51ms	399ms	206ms	186ms
Ridge (500×300)	8ms	89ms	64ms	51ms
Logistic (500×300)	34ms	312ms	198ms	167ms
Elastic Net (500×300)	45ms	380ms	195ms	175ms
SVM (500×300)	42ms	356ms	188ms	162ms

^{Apple M1, Python 3.12, default tolerances}

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Quick Start

pip install pogs

from pogs import solve_lasso
import numpy as np

A = np.random.randn(500, 300)
b = np.random.randn(500)

result = solve_lasso(A, b, lambd=0.1)
print(f"Solved in {result['iterations']} iterations")

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Supported Problems

Problem	Function	Description
Lasso	solve_lasso(A, b, lambd)	L1-regularized least squares
Ridge	solve_ridge(A, b, lambd)	L2-regularized least squares
Elastic Net	solve_elastic_net(A, b, l1, l2)	L1 + L2 regularization
Logistic	solve_logistic(A, y, lambd)	L1-regularized logistic regression
SVM	solve_svm(A, y, lambd)	L2-regularized hinge loss
Huber	solve_huber(A, b, lambd)	Robust regression
NNLS	solve_nonneg_ls(A, b)	Non-negative least squares

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CVXPY Integration

POGS can solve CVXPY problems directly:

import cvxpy as cp
from pogs import pogs_solve

x = cp.Variable(300)
prob = cp.Problem(cp.Minimize(cp.sum_squares(A @ x - b) + 0.1 * cp.norm(x, 1)))

pogs_solve(prob)  # Auto-detects Lasso, uses fast solver

Or register as a named method:

cp.Problem.register_solve("POGS", pogs_solve)
prob.solve(method="POGS")

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How It Works

POGS uses ADMM with closed-form proximal operators. For ML problems, these operators have analytical solutions—no inner iterations needed:

Function	Proximal Operator
½‖·‖²	x/(1+ρ)
λ‖·‖₁	soft_threshold(x, λ/ρ)
λ‖·‖²	x/(1+2λ/ρ)

General-purpose solvers reformulate everything as cone programs. POGS solves the original problem directly.

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Next Steps

• Get Started

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  Install POGS and run your first optimization

  Installation

• Examples

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  Step-by-step examples for each problem type

  Examples

• API Reference

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  Full documentation of all functions

  API

• Source Code

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  Contribute or report issues

  GitHub

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Citation

@article{fougner2018pogs,
  title={Parameter selection and preconditioning for a graph form solver},
  author={Fougner, Christopher and Boyd, Stephen},
  journal={Emerging Applications of Control and Systems Theory},
  pages={41--61},
  year={2018},
  publisher={Springer}
}