On solution sets of nonconvex Darboux problems and applications to optimal control with endpoint constraints

Author:

Tuan H. D.

Abstract

AbstractWe prove a continuous version of a relaxation theorem for the nonconvex Darboux problem xlt ε F(t, τ, x, xt, xτ). This result allows us to use Warga's open mapping theorem for deriving necessary conditions in the form of a maximum principle for optimization problems with endpoint constraints. Neither constraint qualification nor regularity assumption is supposed.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics

Reference56 articles.

1. [41] Tuan H. D. , “Asymptotic construction of solutions to differentiable systems with multi-valued right hand side”, Ph.D. thesis, Odessa state univesity, 1990 (in Russian).

2. A Sobolev space and a Darboux problem

3. Differential Inclusions

4. Optimization with partial differential equations in dieudonné-rashevsky form and conjugate problems

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