Geodesic
Approximate Penalty Method in Optimal Control Problems for Nonsmooth Singular Systems
Matematičeskie zametki, Tome 76 (2004) no. 6, pp. 893-904

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We consider an abstract optimal control problem with additional constraints and nonsmooth terms, but without the requirement that both the state equation on the set of admissible controls and the extremum problem be solvable. We use the approximate penalty method proposed here to find an approximate (in the weak sense) solution of the problem. As an example, we consider the optimal control problem for a singular nonlinear elliptic type equation. 
@article{MZM_2004_76_6_a9,
     author = {S. Ya. Serovaǐskiǐ},
     title = {Approximate {Penalty} {Method} in {Optimal} {Control} {Problems} for {Nonsmooth} {Singular} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {893--904},
     publisher = {mathdoc},
     volume = {76},
     number = {6},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_6_a9/}
}
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S. Ya. Serovaǐskiǐ. Approximate Penalty Method in Optimal Control Problems for Nonsmooth Singular Systems. Matematičeskie zametki, Tome 76 (2004) no. 6, pp. 893-904. http://geodesic.mathdoc.fr/item/MZM_2004_76_6_a9/