Mathematical Programming: Series A and B
The upper and lower second order directional derivatives of a sup-type function
Mathematical Programming: Series A and B
Optimality conditions for some nonqualified problems of distributed control
SIAM Journal on Control and Optimization
Optimal control of semilinear multistate systems with state constraints
SIAM Journal on Control and Optimization
Second order necessary optimality conditions for minimizing a sup-type function
Mathematical Programming: Series A and B
SIAM Journal on Control and Optimization
Perturbed Optimization in Banach Spaces III: Semi-infinite Optimization
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Necessary Optimality Conditions for Control Problems and the Stone--Cech Compactification
SIAM Journal on Control and Optimization
Minimax Control of Parabolic Systems with State Constraints
SIAM Journal on Control and Optimization
Optimal Control Problems with Mixed Control-State Constraints
SIAM Journal on Control and Optimization
Pontryagin's Principle For Local Solutions of Control Problems with Mixed Control-State Constraints
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Mathematical Programming: Series A and B
SIAM Journal on Optimization
SIAM Journal on Control and Optimization
Error estimates for parabolic optimal control problems with control and state constraints
Computational Optimization and Applications
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In this paper we study the optimal control problem of the heat equation with a cubic nonlinearity by a distributed control over a subset of the domain, in the presence of a state constraint. The latter is integral over the space and has to be satisfied each time. Using for the first time the technique of alternative optimality systems in the context of optimal control of partial differential equations, we show that both the control and multiplier are continuous in time. Under some natural geometric hypotheses, we can prove that extended polyhedricity holds, allowing us to obtain no-gap second-order optimality conditions, that characterize quadratic growth. An expansion of the value function and of approximate solutions can be computed for a directional perturbation of the right-hand side of the state equation.