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Generalized Euler-Lagrange equation for nonsmooth calculus of variations. (English) Zbl 1281.70023

Summary: In this paper, we first introduce a novel generalized derivative and obtain the generalized first-order Taylor expansion of the nonsmooth functions. Then we derive the generalized Euler-Lagrange equation for the nonsmooth calculus of variations and solve this equation by using Chebyshev pseudospectral method, approximately. Finally, the optimal solutions of some problems in the nonsmooth calculus of variations are approximated.

MSC:

70H03 Lagrange’s equations
49J52 Nonsmooth analysis
49K20 Optimality conditions for problems involving partial differential equations
49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
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