A generalized multidirectional mean value inequality and dynamic optimization. (3rd July 2019)

• Record Type: Journal Article
• Authors: Kipka, R.; Ledyaev, Yuri
• Is Part Of: Optimization. Volume 68:Number 7(2019)
• Page Start: 1365
• Page End: 1389
• Publication Date: 2019-07-03
• Subjects: Nonsmooth analysis -- variational analysis -- dynamic optimization -- calculus of variations; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1638388
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: We consider a general calculus of variations problem with lower semicontinuous data which includes an optimal control problem with a dynamic differential inclusion constraint as a particular case. We provide a new approach to the derivation of necessary optimality conditions for such a problem, based on a new variant of the multidirectional mean-value inequality for smooth Banach spaces. The multidirectional mean-value inequality is a result in nonlinear and nonsmooth analysis which provides estimates for the minimum difference in function values between a closed convex subset of a Banach space E and a point x 0 ∈ E .