English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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

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