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$$L^\infty $$ L ∞ -Stability of a Parametric Optimal Control Problem Governed by Semilinear Elliptic Equations
Applied Mathematics and Optimization ( IF 1.8 ) Pub Date : 2020-03-03 , DOI: 10.1007/s00245-020-09664-5 Bui Trong Kien , Nguyen Quoc Tuan , Ching-Feng Wen , Jen-Chih Yao
中文翻译:
$$L^\infty $$ L ∞ -半线性椭圆方程控制的参数最优控制问题的稳定性
更新日期:2020-03-03
Applied Mathematics and Optimization ( IF 1.8 ) Pub Date : 2020-03-03 , DOI: 10.1007/s00245-020-09664-5 Bui Trong Kien , Nguyen Quoc Tuan , Ching-Feng Wen , Jen-Chih Yao
This paper studies local stability of a parametric optimal control problem governed by semilinear elliptic equations with mixed pointwise constraints. We show that if the unperturbed problem satisfies the strictly nonnegative second-order optimality conditions, then the solution map is upper Hölder continuous in \(L^\infty \)-norm of control variable.
中文翻译:
$$L^\infty $$ L ∞ -半线性椭圆方程控制的参数最优控制问题的稳定性
本文研究了由具有混合逐点约束的半线性椭圆方程控制的参数最优控制问题的局部稳定性。我们证明,如果未扰动问题满足严格非负二阶最优性条件,则解图在控制变量的\(L^\infty \) -范数上是上 Hölder 连续的。