Open AccessA new proof of the dual optimization problem and its application to the optimal material distribution of SiC/graphene composite
Author(s) -
JiHuan He
Publication year - 2020
Publication title -
reports in mechanical engineering
Language(s) - English
Resource type - Journals
ISSN - 2683-5894
DOI - 10.31181/rme200101187h
Subject(s) - dual (grammatical number) , graphene , duality (order theory) , constraint (computer aided design) , composite number , mathematical optimization , simple (philosophy) , optimization problem , mathematics , computer science , materials science , nanotechnology , algorithm , combinatorics , geometry , art , philosophy , literature , epistemology
This paper presents a simple and direct proof of the dual optimization problem. The stationary conditions of the original and the dual problems are exactly equivalent, and the duality gap can be completely eliminated in the dual problem, where the maximal or minimal value is solved together with the stationary conditions of the dual problem and the original constraints. As an illustration, optimization of SiC/graphene composite is addressed with an objective of maximizing certain material properties under the constraint of a given strength.