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

This paper presents a piecewise convexification method to approximate thewhole approximate optimal solution set of non-convex optimization problems withbox constraints. In the process of box division, we first classify thesub-boxes and only continue to divide only some sub-boxes in the subsequentdivision. At the same time, applying the $\alpha$-based Branch-and-Bound({\rm$\alpha$BB}) method, we construct a series of piecewise convex relaxsub-problems, which are collectively called the piecewise convexificationproblem of the original problem. Then, we define the (approximate) solution setof the piecewise convexification problem based on the classification result ofsub-boxes. Subsequently, we derive that these sets can be used to approximatethe global solution set with a predefined quality. Finally, a piecewiseconvexification algorithm with a new selection rule of sub-box for the divisionand two new termination tests is proposed. Several instances verify that thesetechniques are beneficial to improve the performance of the algorithm.

A Modification Piecewise Convexification Method for Box-Constrained Non-Convex Optimization Programs