Geodesic
Singular optimal controls in the distributed problems and Volterra functional-operator equations
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 39 (2012) no. 1, pp. 128-129

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It is showed that for a broad class of distributed optimization problems a sufficiently typical condition is strong degeneration of the singular controls, when together with a first-order necessary optimality conditions (for example, maximum principle) a second-order necessary optimality conditions also degenerates. It is described a general conclusion scheme of necessary optimality conditions for strong degenerated singular controls.
Keywords: distributed optimization problems, necessary optimality conditions, singular controls, strong degeneration, Volterra functional-operator equations. 
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     author = {V. I. Sumin},
     title = {Singular optimal controls in the distributed problems and {Volterra} functional-operator equations},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
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     url = {http://geodesic.mathdoc.fr/item/IIMI_2012_39_1_a61/}
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V. I. Sumin. Singular optimal controls in the distributed problems and Volterra functional-operator equations. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 39 (2012) no. 1, pp. 128-129. http://geodesic.mathdoc.fr/item/IIMI_2012_39_1_a61/