What is it about?
The main goal of this paper is to introduce necessary efficiency conditions for a class of multi-time vector fractional variational problems with nonlinear equality and inequality constraints involving higher order partial derivatives. We consider the multi-time multiobjective variational problem (MFP) of minimizing a vector of path independent curvilinear integral functionals quotients subject to PDE and/or PDI constraints, developing an optimization theory on the higher order jet bundles.
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Why is it important?
This kind of optimization problems arise in large areas of research where the partial derivatives of order higher than one or two are required. The objective functions used in this paper have an essential role in mathematical modeling of certain processes in relation with engines, robotics, and so forth.
Perspectives
Our study is strongly motivated by its applications, especially in mechanical engineering, where the path independent curvilinear integral objectives are extensively used due to their physical meaning as mechanical work. We introduced and studied a new class of multi-time vector fractional variational problems involving higher order partial derivatives. Within this framework, we formulated and proved necessary efficiency conditions for (MFP), developing an optimization theory on the higher order jet bundles.
Professor Savin Treanta
Universitatea Politehnica din Bucuresti
Read the Original
This page is a summary of: Multiobjective Fractional Variational Problem on Higher-Order Jet Bundles, Communications in Mathematics and Statistics, June 2016, Springer Science + Business Media,
DOI: 10.1007/s40304-016-0087-0.
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