Construction and Iteration-Complexity of Primal Sequences in Alternating Minimization Algorithms

Quoc Tran-Dinh

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arXiv · 1511.03305

Construction and Iteration-Complexity of Primal Sequences in Alternating Minimization Algorithms

Quoc Tran-Dinh

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Abstract

We introduce a new weighted averaging scheme using "Fenchel-type" operators to recover primal solutions in the alternating minimization-type algorithm (AMA) for prototype constrained convex optimization. Our approach combines the classical AMA idea in \cite{Tseng1991} and Nesterov's prox-function smoothing technique without requiring the strong convexity of the objective function. We develop a new non-accelerated primal-dual AMA method and estimate its primal convergence rate both on the objective residual and on the feasibility gap. Then, we incorporate Nesterov's accelerated step into this algorithm and obtain a new accelerated primal-dual AMA variant endowed with a rigorous convergence rate guarantee. We show that the worst-case iteration-complexity in this algorithm is optimal (in the sense of first-oder black-box models), without imposing the full strong convexity assumption on the objective.

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BibTeX RIS

Quoc Tran-Dinh. 2015-11-10. Construction and Iteration-Complexity of Primal Sequences in Alternating Minimization Algorithms. https://arxiv.org/abs/1511.03305

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