Papers › Proportional-Integral Projected Gradient Method for Conic Optimization
Proportional-Integral Projected Gradient Method for Conic Optimization
Yue Yu, Purnanand Elango, Ufuk Topcu, Behçet Açıkmeşe
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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/k²). Further, unlike any existing first-order methods, PIPG also improves the convergence rate of the constraint violation to O(1/k³). We demonstrate the application of PIPG in constrained optimal control problems.
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