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.
Op- timal control of a non-smooth semilinear elliptic equation.Mathematical Control and Related Fields, 8(1):247–276, 2018
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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.