A Universal Accelerated Primal–Dual Method for Convex Optimization Problems

Hao Luo ()
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Hao Luo: Chongqing Normal University

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 1, No 11, 280-312

Abstract: Abstract This work presents a universal accelerated primal–dual method for affinely constrained convex optimization problems. It can handle both Lipschitz and Hölder gradients but does not need to know the smoothness level of the objective function. In line search part, it uses dynamically decreasing parameters and produces approximate Lipschitz constant with moderate magnitude. In addition, based on a suitable discrete Lyapunov function and tight decay estimates of some differential/difference inequalities, a universal optimal mixed-type convergence rate is established. Some numerical tests are provided to confirm the efficiency of the proposed method.

Keywords: Convex optimization; Primal–dual method; Mixed-type estimate; Optimal complexity; Bregman divergence; Lyapunov function; 65B99; 68Q25; 90C25 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02394-6

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