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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

A new decomposition optimization algorithm, called \textit{path-followinggradient-based decomposition}, is proposed to solve separable convexoptimization problems. Unlike path-following Newton methods considered in theliterature, this algorithm does not requires any smoothness assumption on theobjective function. This allows us to handle more general classes of problemsarising in many real applications than in the path-following Newton methods.The new algorithm is a combination of three techniques, namely smoothing,Lagrangian decomposition and path-following gradient framework. The algorithmdecomposes the original problem into smaller subproblems by using dualdecomposition and smoothing via self-concordant barriers, updates the dualvariables using a path-following gradient method and allows one to solve thesubproblem in parallel. Moreover, the algorithmic parameters are updatedautomatically without any tuning strategy as in augmented Lagrangianapproaches. We prove the global convergence of the new algorithm and analyzeits local convergence rate. Then, we modify the proposed algorithm by applyingNesterov's accelerating scheme to get a new variant which has a better localconvergence rate. Finally, we present preliminary numerical tests that confirmthe theory development.

Path-Following Gradient-Based Decomposition Algorithms For Separable Convex Optimization