Lower semicontinuity of the solution map to a parametric elliptic optimal control problem with mixed pointwise constraints

DOI10.1080/02331934.2013.853060zbMath1312.49024OpenAlexW2094596689MaRDI QIDQ5248234

Arnd Rösch, Vu Huu Nhu, Bui Trong Kien

Publication date: 28 April 2015

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331934.2013.853060

zbMATH Keywords

lower semicontinuityelliptic equationparametric optimal controlparametric variational inequalitysolution stability

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Optimality conditions for problems involving partial differential equations (49K20) Variational inequalities (49J40) Sensitivity, stability, parametric optimization (90C31) Control/observation systems governed by partial differential equations (93C20) Navier-Stokes equations for incompressible viscous fluids (76D05) Multivariable systems, multidimensional control systems (93C35) Linear systems in control theory (93C05) Regularity of solutions in optimal control (49N60) Synthesis problems (93B50) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (8)

Solution stability to parametric distributed optimal control problems with finite unilateral constraints ⋮ Upper semicontinuity of the solution map to a parametric boundary optimal control problem with unbounded constraint sets ⋮ Locally Lipschitz stability of a parametric semilinear elliptic optimal control problem with mixed constraints ⋮ Locally Hölder Continuity of the Solution Map to a Boundary Control Problem with Finite Mixed Control-State Constraints ⋮ On the semicontinuity of the solution map to a parametric boundary control problem ⋮ Second-order optimality conditions and solution stability to optimal control problems governed by stationary Navier-Stokes equations ⋮ \(L^\infty\)-stability of a parametric optimal control problem governed by semilinear elliptic equations ⋮ Upper semicontinuity of the solution map to a parametric elliptic optimal control problem

Cites Work

• Unnamed Item
• Lower semicontinuity of the solution map to a parametric generalized variational inequality in reflexive Banach spaces
• Functional analysis, Sobolev spaces and partial differential equations
• Optimal control of PDEs with regularized pointwise state constraints
• Lipschitz stability for elliptic optimal control problems with mixed control-state constraints
• On two numerical methods for state-constrained elliptic control problems

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