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

The auxiliary problem principle of augmented Lagrangian (APP-AL), proposed byCohen and Zhu (1984), aims to find the solution of a constrained optimizationproblem through a sequence of auxiliary problems involving augmentedLagrangian. The merits of this approach are two folds. First, the core functionis usually separable, which makes the subproblems at each step decomposable andparticularly attractive for parallel computing. Second, the choice of the corefunction is quite flexible. Consequently, by carefully specifying thisfunction, APP-AL may reduce to some standard optimization algorithms. In thispaper, we pursue enhancing such flexibility by allowing the core function to benon-identical at each step of the algorithm, and name it varying auxiliaryproblem principle (VAPP-AL). Depending on the problem structure, the varyingcore functions in VAPP-AL can be adapted to design new flexible and suitablealgorithm for parallel and distributed computing. The convergence and O(1/t)convergence rate of VAPP-AL for convex problem with coupling objective andconstraints is proved. Moreover, if this function is specialized to bequadratic, an o(1/t) convergence rate can be established. Interestingly, thenew VAPP framework can cover several variants of Jacobian type augmentedLagrangian decomposition methods as special cases. Furthermore, our techniqueworks for the convex problem with nonseparable objective and multi-blockscoupled linear constraints, which usually can not be handled by ADMM.

Auxiliary Problem Principle of augmented Lagrangian with Varying Core Functions for Large-Scale Structured Convex Problems