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/

Zendy Plus

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

Zendy Tools

Zendy Open

This paper presents a canonical dual approach for solving a nonconvex globaloptimization problem governed by a sum of fourth-order polynomial and alog-sum-exp function. Such a problem arises extensively in engineering andsciences. Based on the canonical duality-triality theory, this nonconvexproblem is transformed to an equivalent dual problem, which can be solvedeasily under certain conditions. We proved that both global minimizer and thebiggest local extrema of the primal problem can be obtained analytically fromthe canonical dual solutions. As two special cases, a quartic polynomialminimization and a minimax problem are discussed. Existence conditions arederived, which can be used to classify easy and relative hard instances.Applications are illustrated by several nonconvex and nonsmooth examples.

Global Solutions to Nonconvex Optimization of 4th-Order Polynomial and Log-Sum-Exp Functions