Locally Lipschitz Stability of a Parametric Semilinear Elliptic Optimal Control Problem with Mixed Constraints

Article Mathematics, Applied

Error Estimates for Approximate Solutions to Seminlinear Elliptic Optimal Control Problems with Nonlinear and Mixed Constraints

B. T. Kien et al.

Summary: This paper provides sufficient conditions for convergence of approximate solutions to semilinear elliptic optimal control problems with mixed pointwise constraints. Discrete optimal control problems are constructed using the finite element method in the form of full control discretization. It is shown that if the strictly second-order sufficient condition is valid, then error estimates between approximate solutions of discrete optimal control problems and optimal solutions of the original problem are obtained.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION (2022)

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Article Mathematics, Applied

L∞-Stability of a Parametric Optimal Control Problem Governed by Semilinear Elliptic Equations

Bui Trong Kien et al.

Summary: This paper investigates the local stability of a parametric optimal control problem governed by semilinear elliptic equations with mixed pointwise constraints. It demonstrates that the solution map is upper Holder continuous in the L infinity-norm of the control variable if the unperturbed problem satisfies the strictly nonnegative second-order optimality conditions.

APPLIED MATHEMATICS AND OPTIMIZATION (2021)

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Article Mathematics, Applied

SOLUTION STABILITY TO PARAMETRIC DISTRIBUTED OPTIMAL CONTROL PROBLEMS WITH FINITE UNILATERAL CONSTRAINTS

Nguyen Hai Son

Summary: This paper investigates the stability of solution map for a parametric control problem with finite unilateral constraints governed by semilinear elliptic equations. By utilizing first-order necessary optimality conditions, the paper establishes sufficient conditions for the solution map to be upper semicontinuous with respect to parameters.

EVOLUTION EQUATIONS AND CONTROL THEORY (2021)

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Article Mathematics