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Proportional-integral projected gradient method for conic optimization
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DOI：10.1016/j.automatica.2022.110359.png)
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Abstract
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Conic optimization is the minimization of a differentiable convex objective function subject to conic constraints. We propose a novel primal-dual first-order method for conic optimization, named proportional-integral projected gradient method (PIPG). PIPG ensures that both the primal-dual gap and the constraint violation converge to zero at the rate of O(1/k), where k is the number of iterations. If the objective function is strongly convex, PIPG improves the convergence rate of the primal-dual gap to O(1/k(2)). Further, unlike any existing first-order methods, PIPG also improves the convergence rate of the constraint violation to O(1/k(3)). We demonstrate the application of PIPG in constrained optimal control problems. (C) 2022 Elsevier Ltd. All rights reserved.
Keywords:
Convex optimization
First-order methods
Optimal control
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