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Matrix-free convex optimization modeling. (English) Zbl 1354.90092
Goldengorin, Boris (ed.), Optimization and applications in control and data sciences. In honor of Boris T. Polyak’s 80th birthday. Selected papers based on the presentations at the international conference, Moscow, Russia, May, 13–15, 2015. Cham: Springer (ISBN 978-3-319-42054-7/hbk; 978-3-319-42056-1/ebook). Springer Optimization and Its Applications 115, 221-264 (2016).
Summary: 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.
For the entire collection see [Zbl 1356.93004].

MSC:
90C25 Convex programming
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