Computational Optimization and Applications
Optimal Control for the Thermistor Problem
SIAM Journal on Control and Optimization
Optimal Control of a Parabolic Equation with Time-Dependent State Constraints
SIAM Journal on Control and Optimization
Stability of semilinear elliptic optimal control problems with pointwise state constraints
Computational Optimization and Applications
Computational Optimization and Applications
On the optimal control of the Schlögl-model
Computational Optimization and Applications
Computational Optimization and Applications
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Second-order sufficient optimality conditions are established for the optimal control of semilinear elliptic and parabolic equations with pointwise constraints on the control and the state. In contrast to former publications on this subject, the cone of critical directions is the smallest possible in the sense that the second-order sufficient conditions are the closest to the associated necessary ones. The theory is developed for elliptic distributed controls in domains up to dimension three. Moreover, problems of elliptic boundary control and parabolic distributed control are discussed in spatial domains of dimension two and one, respectively.