# Matrix-Free Convex Optimization Modeling

@article{Diamond2015MatrixFreeCO, title={Matrix-Free Convex Optimization Modeling}, author={Steven Diamond and Stephen P. Boyd}, journal={arXiv: Optimization and Control}, year={2015}, pages={221-264} }

We introduce a convex optimization modeling framework that transforms a convex optimization problem expressed in a form natural and convenient for the user into an equivalent cone program in a way that preserves fast linear transforms in the original problem. By representing linear functions in the transformation process not as matrices, but as graphs that encode composition of linear operators, we arrive at a matrix-free cone program, i.e., one whose data matrix is represented by a linear…

## 28 Citations

### Differentiating through a cone program

- Computer Science, MathematicsJournal of Applied and Numerical Optimization
- 2019

We consider the problem of efficiently computing the derivative of the solution map of a convex cone program, when it exists. We do this by implicitly differentiating the residual map for its…

### Differentiating Through a Conic Program

- Computer Science, Mathematics
- 2019

We consider the problem of efficiently computing the derivative of the solution map of a convex cone program, when it exists. We do this by implicitly differentiating the residual map for its…

### O C ] 5 J un 2 01 9 Differentiating Through a Cone Program

- Computer Science, Mathematics
- 2019

We consider the problem of efficiently computing the derivative of the solution map of a convex cone program, when it exists. We do this by implicitly differentiating the residual map for its…

### The Symbolic Interior Point Method

- Computer ScienceAAAI
- 2017

This work develops an engine that can fully leverage the structure of symbolic representations to solve convex linear and quadratic optimization problems and demonstrates the flexibility of the resulting symbolic-numeric optimizer on decision making and compressed sensing tasks with millions of non-zero entries.

### O C ] 2 7 M ay 2 01 9 Differentiating Through a Cone Program

- Computer Science, Mathematics
- 2019

An open-source Python implementation of the method that solves a cone program and returns the derivative and its adjoint as abstract linear maps is presented, which can be easily integrated into software systems for automatic differentiation.

### A Rewriting System for Convex Optimization Problems

- Computer ScienceArXiv
- 2017

A modular rewriting system for translating optimization problems written in a domain-specific language to forms compatible with low-level solver interfaces, which makes it easy to match problems to solvers well-suited for them and to support solvers with a wide variety of standard forms.

### A First-Order Numerical Algorithm without Matrix Operations

- Computer Science
- 2022

An easy-to-compute decomposition method to solve sparse linear systems that arise in conic optimization problems and is compared with the state-of-the-art first-order solvers.

### Explorer The Symbolic Interior Point Method

- Computer Science
- 2016

This work develops an engine that can fully leverage the structure of symbolic representations to solve convex linear and quadratic optimization problems and demonstrates the flexibility of the resulting symbolic-numeric optimizer on decision making and compressed sensing tasks with millions of non-zero entries.

### Stochastic Matrix-Free Equilibration

- Computer ScienceJ. Optim. Theory Appl.
- 2017

We present a novel method for approximately equilibrating a matrix using only multiplication by the matrix and its transpose. Our method is based on convex optimization and projected stochastic…

### A New Architecture for Optimization Modeling Frameworks

- Computer Science2016 6th Workshop on Python for High-Performance and Scientific Computing (PyHPC)
- 2016

We propose a new architecture for optimization modeling frameworks in which solvers are expressed as computation graphs in a framework like TensorFlow rather than as standalone programs built on a…

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