Differentiation of operators and optimality conditions in category interpretation
The author considers a system described by a nonlinear elliptic equation with large values of the nonlinearity parameter in which the domain dimension the control-state mapping is not Gâteaux differentiable. For this reason, one cannot immediately differentiate the optimality criterion and establish necessary optimality conditions by classical methods. Fortunately, the mentioned mapping is extendedly differentiable, allowing one to obtain in this way optimality conditions imposing no constraints on system parameters. An interpretation is also provided for the optimality conditions in terms of classical and extended derivatives within the theory of categories.
scientific article; zbMATH DE number 5673451
scientific article