Nonconvex optimal control of nonlinear monotone parabolic systems
Systems & Control Letters
Convergent computational method for relaxed optimal control problems
Journal of Optimization Theory and Applications
Approximation of relaxed nonlinear parabolic optimal control problems
Journal of Optimization Theory and Applications
Mixed Frank-Wolfe penalty method with applications to nonconvex optimal control problems
Journal of Optimization Theory and Applications
Optimization: algorithms and consistent approximations
Optimization: algorithms and consistent approximations
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We consider an optimal control problem defined by semilinear parabolic partial differential equations, with convex control constraints. Since this problem may have no classical solutions, we also formulate it in relaxed form. The classical problem is then discretized by using a finite element method in space and a theta-scheme in time, where the controls are approximated by blockwise constant classical ones. We then propose a discrete, progressively refining, gradient projection method for solving the classical, or the relaxed, problem. We prove that strong accumulation points (if they exist) of sequences generated by this method satisfy the weak optimality conditions for the continuous classical problem, and that relaxed accumulation points (which always exist) satisfy the weak optimality conditions for the continuous relaxed problem. Finally, numerical examples are given.