Optimal control in coefficients for weak variational problems in Hilbert space
Copyright policy )Optimal control in coefficients for weak variational problems in Hilbert space
In this paper we give sufficient conditions for the existence of solutions of a problem of parametric optimization. We use continuity with respect to a functional parameter of weak solutions of a variational problem in a Hilbert space. We consider a problem of optimization with the control in coefficients of linear parabolic equation as an example. Using results of Spagnolo we characterize the closure of the reachable set. Finally, we construct an example of an optimization problem with the control in coefficients of a parabolic equation which does not have an optimal solution.
- Polish Academy of Learning Poland
- Polish Academy of Sciences Poland
- Systems Research Institute Poland
abstract parabolic equation, optimal control in coefficients, Methods involving semicontinuity and convergence; relaxation, Attainable sets, reachability, regularized problem, Initial value problems for linear higher-order PDEs, variational problems on a Hilbert space, Existence theories for optimal control problems involving partial differential equations, minimizing the cost functional, Higher-order parabolic equations
abstract parabolic equation, optimal control in coefficients, Methods involving semicontinuity and convergence; relaxation, Attainable sets, reachability, regularized problem, Initial value problems for linear higher-order PDEs, variational problems on a Hilbert space, Existence theories for optimal control problems involving partial differential equations, minimizing the cost functional, Higher-order parabolic equations
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).17 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!