Geodesic
On the convergence of the conditional gradient method as applied to the optimization of an elliptic equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 2, pp. 213-228

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The optimal control of a second-order semilinear elliptic diffusion-reaction equation is considered. Sufficient conditions for the convergence of the conditional gradient method are obtained without using assumptions (traditional for optimization theory) that ensure the Lipschitz continuity of the objective functional derivative. The total (over the entire set of admissible controls) preservation of solvability, a pointwise estimate of solutions, and the uniqueness of a solution to the homogeneous Dirichlet problem for a controlled elliptic equation are proved as preliminary results, which are of interest on their own. 
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     author = {A. V. Chernov},
     title = {On the convergence of the conditional gradient method as applied to the optimization of an elliptic equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {213--228},
     publisher = {mathdoc},
     volume = {55},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_2_a6/}
}
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A. V. Chernov. On the convergence of the conditional gradient method as applied to the optimization of an elliptic equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 2, pp. 213-228. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_2_a6/