Weak Lower Semi-continuity of the Optimal Value Function and Applications to Worst-case Robust Optimal Control Problems
نویسندگان
چکیده
Sufficient conditions ensuring weak lower semi-continuity of the optimal value function are presented. To this end, refined inner semi-continuity properties of set-valued maps are introduced which meet the needs of the weak topology in Banach spaces. The results are applied to prove the existence of solutions in various worst-case robust optimal control problems governed by semilinear elliptic partial differential equations.
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