Affiliations: [a] School of Economics and Management, North China Electric Power University, Beijing, China | [b] Beijing Key Laboratory of New Energy and Low-Carbon Development, North China Electric Power University, Beijing, China | [c] Department of Mathematics and Computing Science, Wuyi University, Guangdong, Jiangmen, China
Correspondence:
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Corresponding author: Huicheng Liu, School of Economics and Management, North China Electric Power %****␣jcm-19-jcm190014_temp.tex␣Line␣25␣**** University, Beijing 102206, China. Tel.: +86 10 150 1099 6218; E-mail: [email protected].
Abstract: This paper presents a canonical duality theory for general box constrained nonconvex and nonsmooth optimization problems. The theory is illustrated perfectly by showing mainly a canonical dual transformation and a triality theory. It is proved that the general box constrained nonconvex and nonsmooth optimization problems can be changed into the perfect dual problems, which can be solved easily. The perfect dual transformation is developed for eliminating the duality gap,while the triality theorem studies global and local extreme conditions. Applications and examples are illustrated.
Keywords: Canonical (perfect) dual transformation, triality theory, box constrains, nonconvex and nonsmooth minimization, global and local optimization
