The authors define a generalized derivative as the limit of finite-dimensional directional derivatives of the control-to-state map and use it to obtain first- and second-order necessary optimality conditions for a box-constrained problem governed by an exponential semilinear elliptic equation.
An elliptic semilinear equation with source term involving boundary measures: The subcritical case.Revista Matem´ atica Iberoamericana, 16(3):477–513, 2000
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Generalized Differentiability and Second-Order Necessary Optimality Conditions for an Elliptic Optimal Control Problem with Exponential Nonlinearity and Discrete Measures
The authors define a generalized derivative as the limit of finite-dimensional directional derivatives of the control-to-state map and use it to obtain first- and second-order necessary optimality conditions for a box-constrained problem governed by an exponential semilinear elliptic equation.