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. 
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/
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