Geodesic
Methods of steepest and hypodifferential descent in one problem of calculus of variations
Numerical methods and programming, Tome 13 (2012) no. 1, pp. 197-217

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A detailed description of the solution of a variational problem for a functional dependent on the third-order derivative is given. The constrained optimization problem under consideration is reduced using the technique of exact penalty functions to a problem of unconstrained optimization. In order to construct an exact penalty function, the “direct” numerical methods of steepest and hypodifferential descent are proposed.
Keywords: nonsmooth analysis; nondifferentiable optimization; subdifferential; codifferential; exact penalty function; calculus of variations. 
@article{VMP_2012_13_1_a20,
     author = {G. Sh. Tamasyan},
     title = {Methods of steepest and hypodifferential descent in one problem of calculus of variations},
     journal = {Numerical methods and programming},
     pages = {197--217},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2012_13_1_a20/}
}
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G. Sh. Tamasyan. Methods of steepest and hypodifferential descent in one problem of calculus of variations. Numerical methods and programming, Tome 13 (2012) no. 1, pp. 197-217. http://geodesic.mathdoc.fr/item/VMP_2012_13_1_a20/