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• W3088809084 abstract "This work is concerned with second-order necessary and sufficient optimality conditions for optimal control of a non-smooth semilinear elliptic partial differential equation, where the nonlinearity is the non-smooth max-function and thus the associated control-to-state operator is in general not Gâteaux-differentiable. In addition to standing assumptions, two main hypotheses are imposed. The first one is the Gâteaux-differentiability at the considered control of the objective functional and it is precisely characterized by the vanishing of an adjoint state on the active set. The second one is a structural assumption on the 'almost' active sets, i.e., the sets of all points at which the values of the interested state are 'close' to the non-differentiability point of the max-function. We then derive a 'no-gap' theory of second-order optimality conditions in terms of an abstract curvature functional, i.e., for which the only change between necessary or sufficient second-order optimality conditions is between a strict and non strict inequality." @default.
• W3088809084 created "2020-10-01" @default.
• W3088809084 creator A5058708435 @default.
• W3088809084 date "2020-09-25" @default.
• W3088809084 modified "2023-09-27" @default.
• W3088809084 title "On the no-gap second-order optimality conditions for a non-smooth semilinear elliptic optimal control" @default.
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• W3088809084 hasPublicationYear "2020" @default.
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