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Matrix-Free Convex Optimization Modeling

In: Optimization and Its Applications in Control and Data Sciences

Author

Listed:
  • Steven Diamond

    (Stanford University)

  • Stephen Boyd

    (Stanford University)

Abstract

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 operator and its adjoint. This cone program can then be solved by a matrix-free cone solver. By combining the matrix-free modeling framework and cone solver, we obtain a general method for efficiently solving convex optimization problems involving fast linear transforms.

Suggested Citation

  • Steven Diamond & Stephen Boyd, 2016. "Matrix-Free Convex Optimization Modeling," Springer Optimization and Its Applications, in: Boris Goldengorin (ed.), Optimization and Its Applications in Control and Data Sciences, pages 221-264, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-42056-1_7
    DOI: 10.1007/978-3-319-42056-1_7
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    Cited by:

    1. Steven Diamond & Stephen Boyd, 2017. "Stochastic Matrix-Free Equilibration," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 436-454, February.

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