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Fast Solution Methods for Convex Quadratic Optimization of Fractional Differential Equations by Pougkakiotis, Spyridon; Pearson, John W.; Leveque, Santolo; Gondzio, Jacek is a scholarly article available to read on EtoBox.

What is Fast Solution Methods for Convex Quadratic Optimization of Fractional Differential Equations about?

In this paper, we present numerical methods suitable for solving convex quadratic Fractional Differential Equation (FDE) constrained optimization problems, with box constraints on the state and/or control variables. We develop an Alternating Direction Method of Multipliers (ADMM) framework, which uses preconditioned Krylov subspace solvers for the resulting sub-problems. The latter allows us to tackle a range of Partial Differential Equation (PDE) optimization problems with box constraints, posed on space-time domains, that were previously out of the reach of state-of-the-art preconditioners. In particular, by making use of the powerful Generalized Locally Toeplitz (GLT) sequences theory, we show that any existing GLT structure present in the problem matrices is preserved by ADMM, and we propose some preconditioning methodologies that could be used within the solver, to demonstrate the generality of the approach. Focusing on convex quadratic programs with time-dependent 2-dimensional FDE constraints, we derive multilevel circulant preconditioners, which may be embedded within Krylov subspace methods, for solving the ADMM sub-problems. Discretized versions of FDEs involve large dens

Author

Pougkakiotis, Spyridon; Pearson, John W.; Leveque, Santolo; Gondzio, Jacek

Published

2019

Language

EN