Constrained linear-quadratic optimization problems with parameter-dependent entries. (English) Zbl 1528.49028
The author’s abstract: The paper provides strong convergence of solutions to a sequence of linear-quadratic optimization problems defined in an abstract functional framework. Each problem is accompanied by the constraint of reaching a given target within a prescribed precision. We show that the problems are well-posed and characterize their solutions. The main result provides the conditions under which these solutions converge to the minimizer of the limit problem. The generality of the result allows its application to a wide range of problems: elliptic, parabolic, control ones, etc. The examples presented in the paper consider optimal approximate controls of the heat equation and optimal approximate solutions to the Poisson equation.
Reviewer: Roman Šimon Hilscher (Brno)
MSC:
| 49N10 | Linear-quadratic optimal control problems |
| 35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
| 93B05 | Controllability |
| 93C20 | Control/observation systems governed by partial differential equations |
Keywords:
LQ optimization; parametrized PDEs; optimal controls; optimal approximate solutions; convergence of minimizersReferences:
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