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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this article, a class of lower-order smoothed objective penalty functions is introduced to find locally optimal points for constrained optimization problems. The exactness of the new penalty functions is studied. Based on the current locally optimal points, a new class of penalty functions based on filling properties is proposed. This new penalty function can be used to find a better locally optimal point. The exactness and filling properties of this penalty function are proved in this paper. To do this, two algorithms are presented to find the locally and globally optimal points. Additionally, their convergence is proved under some mild conditions. Finally, numerical results are included to illustrate the applicability of the local and global optimization algorithms.

Lower-order smoothed objective penalty functions based on filling properties for constrained optimization problems