Matrix-Free Convex Optimization Modeling

Steven Diamond () and Stephen Boyd ()
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Steven Diamond: Stanford University
Stephen Boyd: Stanford University

A chapter in Optimization and Its Applications in Control and Data Sciences, 2016, pp 221-264 from Springer

Abstract: 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.

Keywords: Convex optimization; Matrix-free optimization; Conic programming; Optimization modeling (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-42056-1_7

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DOI: 10.1007/978-3-319-42056-1_7

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