Minimization of vectors of curvilinear functionals on the second order jet bundle: sufficient efficiency conditions

Strongly motivated by its possible applications in Mechanics, in our previous work (Pitea and Postolache (Optim. Lett. doi: 10.1007/s11590-010-0272-0 , 2011 )), we initiated an optimization theory for the second order jet bundle. We considered the problem of minimization of vectors of curvilinear fu...

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Bibliographic Details
Published inOptimization letters Vol. 6; no. 8; pp. 1657 - 1669
Main Authors Pitea, Ariana, Postolache, Mihai
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.12.2012
Subjects
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
49J35
Multi-objective variational problem
Lagrange 1-form density
Quasiinvexity
Efficiency
58E17
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Summary:Strongly motivated by its possible applications in Mechanics, in our previous work (Pitea and Postolache (Optim. Lett. doi: 10.1007/s11590-010-0272-0 , 2011 )), we initiated an optimization theory for the second order jet bundle. We considered the problem of minimization of vectors of curvilinear functionals (well known as mechanical work), thought as multi-time multi-objective variational problems, subject to PDE and/or PDI constraints. Within this framework, we introduced necessary conditions. As natural continuation of our results in Pitea and Postolache (Optim. Lett. doi: 10.1007/s11590-010-0272-0 , 2011 ), the present work introduces a study of sufficient efficiency conditions. While the background in Sect. 2 is introductory, the theory in Sect. 3 is new as a whole, containing our results.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-011-0357-4