Geodesic
On singular controls in the sense of the pointwise maximum principle in distributed optimization problems
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2010), pp. 70-80

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It is proved that for distributed optimization problems a sufficiently typical situation is strong degeneration of the singular controls in the sense of the pointwise maximum principle, when together with the maximum principle (which is a first order necessary optimality condition in the case of spike-shaped variation) a second order necessary optimality conditions also degenerates. A derivation of constructive necessary optimality conditions for singular controls is suggested.
Keywords: distributed optimization problems, guided Volterra functional equations, pointwise maximum principle, singular controls. 
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     author = {V. I. Sumin},
     title = {On singular controls in the sense of the pointwise maximum principle in distributed optimization problems},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {70--80},
     publisher = {mathdoc},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2010_3_a8/}
}
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V. I. Sumin. On singular controls in the sense of the pointwise maximum principle in distributed optimization problems. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2010), pp. 70-80. http://geodesic.mathdoc.fr/item/VUU_2010_3_a8/