Geodesic
Optimization of loading places and load response functions for stationary systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 4, pp. 633-644

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The problem of optimizing loading places and corresponding load response functions with respect to objects described by systems of loaded ordinary differential equations is solved numerically. Analytical formulas for the gradient of the functional with respect to the optimized load parameters are derived to solve the problem by applying first-order numerical methods. Results of numerical experiments are presented. The approach proposed can also be used to optimize load parameters in distributed systems described by partial differential equations, which are reduced to the considered problem by applying the method of lines. 
@article{ZVMMF_2017_57_4_a4,
     author = {V. M. Abdullayev and K. R. Aida-zade},
     title = {Optimization of loading places and load response functions for stationary systems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {633--644},
     publisher = {mathdoc},
     volume = {57},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a4/}
}
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V. M. Abdullayev; K. R. Aida-zade. Optimization of loading places and load response functions for stationary systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 4, pp. 633-644. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a4/