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Constrained Linear-Quadratic Optimization Problems with Parameter-Dependent Entries

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  • Martin Lazar

    (University of Dubrovnik)

Abstract

The paper provides strong convergence of solutions to a sequence of linear-quadratic (LQ) 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.

Suggested Citation

  • Martin Lazar, 2023. "Constrained Linear-Quadratic Optimization Problems with Parameter-Dependent Entries," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 781-804, August.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:2:d:10.1007_s10957-023-02257-6
    DOI: 10.1007/s10957-023-02257-6
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