Karthik Prakhya, Zimeng Wang, Alp Yurtsever · 2026 · arXiv
DOI: 10.48550/arXiv.2610.28300 · open-access PDF
We propose adaptive primal-dual subgradient methods for constrained convex optimization. Our first method applies an AdaGrad-style step-sizes to the dual problem and recovers primal solutions by averaging the associated Fenchel-type oracle outputs. It achieves $\widetilde{\mathcal{O}}(T^{-1/2})$ convergence for the dual objective residual, primal objective residual, and feasibility gap in the nonsmooth regime, while automatically improving to $\mathcal{O}(T^{-1})$ when the dual objective is smooth. We further develop an accelerated variant, which retains the $\widetilde{\mathcal{O}}(T^{-1/2})$
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